Archiv der Mathematik, ISSN 0003-889X, 2/2019, Volume 112, Issue 2, pp. 149 - 160

Let A be an algebra over a field F of characteristic zero. For every $$n\ge 1$$ n ≥ 1 , let $$\delta _n(A)$$ δ n ( A ) be the number of linearly independent...

Primary 16R10 | Codimension | Polynomial identity | Mathematics, general | Mathematics | 15A69 | Secondary 16P90 | Exponential growth | Central polynomial | MATHEMATICS | CODIMENSION GROWTH | Algebra

Primary 16R10 | Codimension | Polynomial identity | Mathematics, general | Mathematics | 15A69 | Secondary 16P90 | Exponential growth | Central polynomial | MATHEMATICS | CODIMENSION GROWTH | Algebra

Journal Article

Communications in Algebra, ISSN 0092-7872, 05/2015, Volume 43, Issue 5, pp. 1967 - 1982

In this paper we study the growth rates of Artin monoids, and we show that 4 is a universal upper bound. We also show that the generating functions of the...

Right-angled Artin monoids | Coxeter graphs | Growth rate | Artin groups | Recurrence relations | MATHEMATICS | 20M05 | BRAID-GROUPS | 20F36 | 16P90

Right-angled Artin monoids | Coxeter graphs | Growth rate | Artin groups | Recurrence relations | MATHEMATICS | 20M05 | BRAID-GROUPS | 20F36 | 16P90

Journal Article

São Paulo Journal of Mathematical Sciences, ISSN 1982-6907, 12/2016, Volume 10, Issue 2, pp. 219 - 227

This survey is devoted to the construction of several counterexamples that can be given in combinatorial PI-theory when dealing with growth of varieties of...

Primary 16R10 | Codimension | Polynomial identity | Mathematics, general | Mathematics | Exponential growth | 16P90

Primary 16R10 | Codimension | Polynomial identity | Mathematics, general | Mathematics | Exponential growth | 16P90

Journal Article

São Paulo Journal of Mathematical Sciences, ISSN 1982-6907, 12/2016, Volume 10, Issue 2, pp. 263 - 272

We consider non necessarily associative algebras over a field of characteristic zero and their polynomial identities. Here we describe some of the results...

16R10 | Codimension | Polynomial identity | Primary 17A30 | Mathematics, general | Mathematics | Variety | Secondary 16P90 | Almost nilpotent

16R10 | Codimension | Polynomial identity | Primary 17A30 | Mathematics, general | Mathematics | Variety | Secondary 16P90 | Almost nilpotent

Journal Article

Monatshefte für Mathematik, ISSN 0026-9255, 2/2016, Volume 179, Issue 2, pp. 191 - 199

This paper examines the invariants of automorphisms, derivations, and $$q$$ q -skew derivations of finitely generated domains with finite GK dimension. We...

GK dimension | Mathematics, general | 16W25 | Mathematics | Derivations | Automorphisms | Skew derivations | Invariants | 16P90 | MATHEMATICS | ALGEBRAS | CENTRALIZERS | GELFAND-KIRILLOV DIMENSION

GK dimension | Mathematics, general | 16W25 | Mathematics | Derivations | Automorphisms | Skew derivations | Invariants | 16P90 | MATHEMATICS | ALGEBRAS | CENTRALIZERS | GELFAND-KIRILLOV DIMENSION

Journal Article

Algebras and Representation Theory, ISSN 1386-923X, 6/2018, Volume 21, Issue 3, pp. 579 - 587

The Gelfand–Kirillov dimension has gained importance since its introduction as a tool in the study of non-commutative infinite dimensional algebras and their...

Simple ring | 16S32 | Associative Rings and Algebras | 16D60 | Non-associative Rings and Algebras | Simple module | Commutative Rings and Algebras | Mathematics | 16P90 | Gelfand–Kirillov dimension | Algebra

Simple ring | 16S32 | Associative Rings and Algebras | 16D60 | Non-associative Rings and Algebras | Simple module | Commutative Rings and Algebras | Mathematics | 16P90 | Gelfand–Kirillov dimension | Algebra

Journal Article

Communications in Algebra, ISSN 0092-7872, 09/2015, Volume 43, Issue 9, pp. 3823 - 3839

We study polynomial identities of algebras with adjoined external unit. For a wide class of algebras we prove that adjoining external unit element leads to...

Codimension | Primary: 16R10 | Polynomial identity | Fractional PI-exponent | Non-associative unital algebra | Exponential growth | Secondary: 16P90 | MATHEMATICS | CODIMENSION GROWTH | Mathematics - Rings and Algebras

Codimension | Primary: 16R10 | Polynomial identity | Fractional PI-exponent | Non-associative unital algebra | Exponential growth | Secondary: 16P90 | MATHEMATICS | CODIMENSION GROWTH | Mathematics - Rings and Algebras

Journal Article

São Paulo Journal of Mathematical Sciences, ISSN 1982-6907, 6/2019, Volume 13, Issue 1, pp. 158 - 176

To an arbitrary Lie superalgebra L we associate its Jordan double $${\mathcal Jor}(L)$$ J o r ( L ) , which is a Jordan superalgebra. This notion was...

16S32 | Nil-algebras | Wreath product | Growth | 16N40 | Mathematics | Graded algebras | Jordan superalgebras | Self-similar algebras | 16P90 | Lie superalgebra | 17B66 | 17C10 | 17C50 | 17B63 | 17B65 | 17A70 | Mathematics, general | 17B70 | 17C70 | Poisson superalgebras

16S32 | Nil-algebras | Wreath product | Growth | 16N40 | Mathematics | Graded algebras | Jordan superalgebras | Self-similar algebras | 16P90 | Lie superalgebra | 17B66 | 17C10 | 17C50 | 17B63 | 17B65 | 17A70 | Mathematics, general | 17B70 | 17C70 | Poisson superalgebras

Journal Article

Bulletin of Mathematical Sciences, ISSN 1664-3607, 8/2018, Volume 8, Issue 2, pp. 257 - 306

In this article we analyze the notions of amenability and paradoxical decomposition from an algebraic perspective. We consider this dichotomy for locally...

Coarse spaces | 16S99 | Unital $$\mathbb {K}$$ K -algebras | 37A15 | Mathematics | Paradoxical decompositions | Translation algebras | 16P90 | 20F65 | Leavitt path algebras | Følner nets | Mathematics, general | Amenability | 43A07

Coarse spaces | 16S99 | Unital $$\mathbb {K}$$ K -algebras | 37A15 | Mathematics | Paradoxical decompositions | Translation algebras | 16P90 | 20F65 | Leavitt path algebras | Følner nets | Mathematics, general | Amenability | 43A07

Journal Article

Mathematische Zeitschrift, ISSN 0025-5874, 6/2014, Volume 277, Issue 1, pp. 591 - 609

We study the existence of free subalgebras in division algebras, and prove the following general result: if $$A$$ A is a noetherian domain which is countably...

16S10 | GK dimension | 16S85 | Centralizers | Mathematics, general | Mathematics | Free algebras | Division algebras | 16K40 | 16P90 | MATHEMATICS | FREE SUBGROUPS | FRACTIONS | FREE SUBSEMIGROUPS | RINGS | Algebra

16S10 | GK dimension | 16S85 | Centralizers | Mathematics, general | Mathematics | Free algebras | Division algebras | 16K40 | 16P90 | MATHEMATICS | FREE SUBGROUPS | FRACTIONS | FREE SUBSEMIGROUPS | RINGS | Algebra

Journal Article

Advances in Applied Clifford Algebras, ISSN 0188-7009, 9/2017, Volume 27, Issue 3, pp. 2885 - 2897

Let A be a finite dimensional algebra graded by a finite group, and let $$\Gamma $$ Γ be the corresponding smash product. We prove that if A is separably...

Stable module category | Mathematical Methods in Physics | Theoretical, Mathematical and Computational Physics | Oppermann dimension | Applications of Mathematics | Physics, general | Secondary 16S34 | Physics | Primary 16G10 | 16P90 | Representation dimension | Smash product | MATHEMATICS, APPLIED | SELF-INJECTIVE ALGEBRAS | SKEW GROUP-ALGEBRAS | PHYSICS, MATHEMATICAL | Algebra

Stable module category | Mathematical Methods in Physics | Theoretical, Mathematical and Computational Physics | Oppermann dimension | Applications of Mathematics | Physics, general | Secondary 16S34 | Physics | Primary 16G10 | 16P90 | Representation dimension | Smash product | MATHEMATICS, APPLIED | SELF-INJECTIVE ALGEBRAS | SKEW GROUP-ALGEBRAS | PHYSICS, MATHEMATICAL | Algebra

Journal Article

Algebras and Representation Theory, ISSN 1386-923X, 12/2015, Volume 18, Issue 6, pp. 1533 - 1546

Given a finitely generated free monoid X and a morphism ϕ : X → X, we show that one can construct an algebra, which we call an iterative algebra, in a natural...

Iterative algebras | 16W50 | Decidability | Non-associative Rings and Algebras | Lie algebras | Commutative Rings and Algebras | Mathematics | Combinatorics on words | 16P90 | Associative Rings and Algebras | Monomial algebras | Graded nilpotent algebras | 05A05 | Morphic words | Monoids | WORDS | RINGS | PERIODICITY | MATHEMATICS | GROWTH | Algebra

Iterative algebras | 16W50 | Decidability | Non-associative Rings and Algebras | Lie algebras | Commutative Rings and Algebras | Mathematics | Combinatorics on words | 16P90 | Associative Rings and Algebras | Monomial algebras | Graded nilpotent algebras | 05A05 | Morphic words | Monoids | WORDS | RINGS | PERIODICITY | MATHEMATICS | GROWTH | Algebra

Journal Article

Algebras and Representation Theory, ISSN 1386-923X, 10/2014, Volume 17, Issue 5, pp. 1401 - 1412

We study ℤ2-graded identities of Lie superalgebras of the type b(t), t ≥ 2, over a field of characteristic zero. Our main result is that the n-th codimension...

Associative Rings and Algebras | Codimensions | Non-associative Rings and Algebras | Polynomial identity | Fractional PI-exponent | Secondary 16R10 | Commutative Rings and Algebras | Mathematics | Primary 17B01, 16P90 | Exponential growth | Lie superalgebra | MATHEMATICS | ALGEBRAS | CODIMENSION GROWTH | VARIETIES | Algebra | Mathematics - Rings and Algebras

Associative Rings and Algebras | Codimensions | Non-associative Rings and Algebras | Polynomial identity | Fractional PI-exponent | Secondary 16R10 | Commutative Rings and Algebras | Mathematics | Primary 17B01, 16P90 | Exponential growth | Lie superalgebra | MATHEMATICS | ALGEBRAS | CODIMENSION GROWTH | VARIETIES | Algebra | Mathematics - Rings and Algebras

Journal Article

Bulletin of Mathematical Sciences, ISSN 1664-3607, 2018, Volume 8, Issue 2, pp. 257 - 306

In this article we analyze the notions of amenability and paradoxical decomposition from an algebraic perspective. We consider this dichotomy for locally...

Coarse spaces | 20F65 | 16S99 | Leavitt path algebras | Følner nets | 37A15 | Unital \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {K}$$\end{document}K-algebras | Amenability | 43A07 | Paradoxical decompositions | Translation algebras | 16P90

Coarse spaces | 20F65 | 16S99 | Leavitt path algebras | Følner nets | 37A15 | Unital \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {K}$$\end{document}K-algebras | Amenability | 43A07 | Paradoxical decompositions | Translation algebras | 16P90

Journal Article

Algebras and Representation Theory, ISSN 1386-923X, 12/2014, Volume 17, Issue 6, pp. 1843 - 1852

Let k be an algebraically closed field of characteristic zero and let H be a noetherian cocommutative Hopf algebra over k. We show that if H has polynomially...

Non-associative Rings and Algebras | Primitive ideals | 16S30 | Commutative Rings and Algebras | Mathematics | Nullstellensatz | 16P90 | Gelfand-Kirillov dimension | Secondary 16T05 | Associative Rings and Algebras | Cocommutative Hopf algebras | Dixmier-Moeglin equivalence | Primary 16W30 | MATHEMATICS | PRIMITIVE-IDEALS | NOETHERIAN-RINGS | EXTENSIONS | COORDINATE RINGS | Algebra

Non-associative Rings and Algebras | Primitive ideals | 16S30 | Commutative Rings and Algebras | Mathematics | Nullstellensatz | 16P90 | Gelfand-Kirillov dimension | Secondary 16T05 | Associative Rings and Algebras | Cocommutative Hopf algebras | Dixmier-Moeglin equivalence | Primary 16W30 | MATHEMATICS | PRIMITIVE-IDEALS | NOETHERIAN-RINGS | EXTENSIONS | COORDINATE RINGS | Algebra

Journal Article

Selecta Mathematica, ISSN 1022-1824, 10/2014, Volume 20, Issue 4, pp. 1197 - 1212

In 1964, Golod and Shafarevich found that, provided that the number of relations of each degree satisfies some bounds, there exist infinitely dimensional...

16R10 | 16W50 | Golod–Shaferevich algebras | Growth of algebras and the Gelfand–Kirillov dimension | Mathematics, general | 16N40 | Mathematics | 16P40 | 16N20 | 16S15 | 16P90 | 16D25 | MATHEMATICS | BEZOUT | MATHEMATICS, APPLIED | Golod-Shaferevich algebras | POWER-SERIES RINGS | Growth of algebras and the Gelfand-Kirillov dimension | GELFAND-KIRILLOV DIMENSION | Algebra

16R10 | 16W50 | Golod–Shaferevich algebras | Growth of algebras and the Gelfand–Kirillov dimension | Mathematics, general | 16N40 | Mathematics | 16P40 | 16N20 | 16S15 | 16P90 | 16D25 | MATHEMATICS | BEZOUT | MATHEMATICS, APPLIED | Golod-Shaferevich algebras | POWER-SERIES RINGS | Growth of algebras and the Gelfand-Kirillov dimension | GELFAND-KIRILLOV DIMENSION | Algebra

Journal Article

Algebras and Representation Theory, ISSN 1386-923X, 2/2015, Volume 18, Issue 1, pp. 221 - 233

The finite dimensional simple superalgebras play an important role in the theory of PI-algebras in characteristic zero. The main goal of this paper is to...

16R10 | Associative Rings and Algebras | Polynomial identities | Codimensions | Growth | Non-associative Rings and Algebras | Superalgebras | Commutative Rings and Algebras | Mathematics | 16P90 | 16W55 | MATHEMATICS | IDENTITIES | PI-ALGEBRAS | EXPONENTIAL-GROWTH | Algebra

16R10 | Associative Rings and Algebras | Polynomial identities | Codimensions | Growth | Non-associative Rings and Algebras | Superalgebras | Commutative Rings and Algebras | Mathematics | 16P90 | 16W55 | MATHEMATICS | IDENTITIES | PI-ALGEBRAS | EXPONENTIAL-GROWTH | Algebra

Journal Article

中国科学：数学英文版, ISSN 1674-7283, 2013, Volume 56, Issue 8, pp. 1607 - 1618

In this paper, we show that the McKay quiver of a finite subgroup of a general linear group is a regular covering of the McKay quiver of its intersection with...

特殊线性群 | 代数 | 麦 | 颤动 | 交集 | 一般线性群 | 有限子群 | 有限阿贝尔群 | 16S34 | absolute n -complete algebra | Mathematics | Applications of Mathematics | Nakayama translation | McKay quiver | 16G20 | 16P90 | absolute n-complete algebra | MATHEMATICS | MATHEMATICS, APPLIED | COVERINGS | GRAPHS | Computer science | Algebra | Algorithms | Construction | Mathematical analysis | China | Covering | Subgroups | Cylinders | Series (mathematics) | Astronomy

特殊线性群 | 代数 | 麦 | 颤动 | 交集 | 一般线性群 | 有限子群 | 有限阿贝尔群 | 16S34 | absolute n -complete algebra | Mathematics | Applications of Mathematics | Nakayama translation | McKay quiver | 16G20 | 16P90 | absolute n-complete algebra | MATHEMATICS | MATHEMATICS, APPLIED | COVERINGS | GRAPHS | Computer science | Algebra | Algorithms | Construction | Mathematical analysis | China | Covering | Subgroups | Cylinders | Series (mathematics) | Astronomy

Journal Article

Mathematische Zeitschrift, ISSN 0025-5874, 6/2008, Volume 259, Issue 2, pp. 433 - 455

If A is a strongly noetherian graded algebra generated in degree one, then there is a canonically constructed graded ring homomorphism from A to a twisted...

16W50 | Graded ring | 14A22 | noncommutative projective geometry | Mathematics, general | Mathematics | twisted homogeneous coordinate ring | strongly noetherian | 16P90 | Gelfand-Kirillov dimension | 16S38 | Strongly noetherian | Twisted homogeneous coordinate ring | Noncommutative projective geometry | MATHEMATICS | ALGEBRAS | GROWTH | graded ring | QUANTUM P-3

16W50 | Graded ring | 14A22 | noncommutative projective geometry | Mathematics, general | Mathematics | twisted homogeneous coordinate ring | strongly noetherian | 16P90 | Gelfand-Kirillov dimension | 16S38 | Strongly noetherian | Twisted homogeneous coordinate ring | Noncommutative projective geometry | MATHEMATICS | ALGEBRAS | GROWTH | graded ring | QUANTUM P-3

Journal Article

manuscripta mathematica, ISSN 0025-2611, 6/2007, Volume 123, Issue 2, pp. 185 - 203

Let G be the infinite dimensional Grassmann algebra over a field F of characteristic zero and UT 2 the algebra of 2 × 2 upper triangular matrices over F. The...

Geometry | Primary 16R10 | Topological Groups, Lie Groups | Calculus of Variations and Optimal Control; Optimization | Algebraic Geometry | Mathematics, general | Mathematics | Number Theory | Secondary 16P90 | MATHEMATICS | IDENTITIES | T-IDEALS | PI-ALGEBRAS | CODIMENSION GROWTH

Geometry | Primary 16R10 | Topological Groups, Lie Groups | Calculus of Variations and Optimal Control; Optimization | Algebraic Geometry | Mathematics, general | Mathematics | Number Theory | Secondary 16P90 | MATHEMATICS | IDENTITIES | T-IDEALS | PI-ALGEBRAS | CODIMENSION GROWTH

Journal Article

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