Letters in Mathematical Physics, ISSN 0377-9017, 3/2017, Volume 107, Issue 3, pp. 475 - 503

For a noncommutative configuration space whose coordinate algebra is the universal enveloping algebra of a finite-dimensional Lie algebra, it is known how to...

16S32 | 16Txx | Theoretical, Mathematical and Computational Physics | Complex Systems | Noncommutative phase space | 16S30 | Physics | Completed tensor product | Geometry | Hopf algebroid | Deformed derivative | Group Theory and Generalizations | Universal enveloping algebra | 16S35 | QUANTUM GROUPOIDS | PHYSICS, MATHEMATICAL | BIALGEBROIDS | DEFORMATION | Derivatives (Financial instruments) | Algebra

16S32 | 16Txx | Theoretical, Mathematical and Computational Physics | Complex Systems | Noncommutative phase space | 16S30 | Physics | Completed tensor product | Geometry | Hopf algebroid | Deformed derivative | Group Theory and Generalizations | Universal enveloping algebra | 16S35 | QUANTUM GROUPOIDS | PHYSICS, MATHEMATICAL | BIALGEBROIDS | DEFORMATION | Derivatives (Financial instruments) | Algebra

Journal Article

Algebras and Representation Theory, ISSN 1386-923X, 8/2018, Volume 21, Issue 4, pp. 703 - 716

We give a description of the category of restricted Lie algebras over a field 𝕜 $\Bbbk $ of prime characteristic by means of monadic decomposition of the...

Monads | Restricted Lie algebras | Associative Rings and Algebras | Non-associative Rings and Algebras | Secondary 16S30 | Commutative Rings and Algebras | Mathematics | Primary 18C15 | MATHEMATICS | HOPF-ALGEBRAS | Computer science | Algebra

Monads | Restricted Lie algebras | Associative Rings and Algebras | Non-associative Rings and Algebras | Secondary 16S30 | Commutative Rings and Algebras | Mathematics | Primary 18C15 | MATHEMATICS | HOPF-ALGEBRAS | Computer science | Algebra

Journal Article

São Paulo Journal of Mathematical Sciences, ISSN 1982-6907, 6/2019, Volume 13, Issue 1, pp. 342 - 369

Using combinatorial methods we study the structural coefficients of the formal homogeneous universal enveloping algebra $$\widehat{U}_h({\mathfrak {sl}}_2) $$...

Universal enveloping algebras | 17B45 | Poincaré–Birkoff–Witt | 16S30 | Mathematics, general | 05A19 | Mathematics | Combinatorics

Universal enveloping algebras | 17B45 | Poincaré–Birkoff–Witt | 16S30 | Mathematics, general | 05A19 | Mathematics | Combinatorics

Journal Article

São Paulo Journal of Mathematical Sciences, ISSN 1982-6907, 12/2018, Volume 12, Issue 2, pp. 246 - 251

We use that the n-sphere for $$n\ge 2$$ n≥2 is simply-connected to prove the Poincaré-Birkhoff-Witt Theorem.

Mathematics, general | Mathematics | Universal enveloping algebra | Symmetric group | 16S30 | Poincaré-Birkhoff-Witt

Mathematics, general | Mathematics | Universal enveloping algebra | Symmetric group | 16S30 | Poincaré-Birkhoff-Witt

Journal Article

Mathematische Zeitschrift, ISSN 0025-5874, 4/2017, Volume 285, Issue 3, pp. 685 - 705

We consider the Lie algebra $$\mathfrak {g}$$ g of a simple, simply connected algebraic group over a field of large positive characteristic. For each nilpotent...

Restricted Lie algebras | Skryabin’s equivalence | Primary 17B50 | Secondary 16S30 | 17B08 | Mathematics, general | Mathematics | Finite W -algebras | Modular representation theory | Finite W-algebras | LIE-ALGEBRAS | MATHEMATICS | PRIMITIVE-IDEALS | REPRESENTATIONS | Skryabin's equivalence | NILPOTENT ORBITS | REDUCTIVE GROUPS | Algebra

Restricted Lie algebras | Skryabin’s equivalence | Primary 17B50 | Secondary 16S30 | 17B08 | Mathematics, general | Mathematics | Finite W -algebras | Modular representation theory | Finite W-algebras | LIE-ALGEBRAS | MATHEMATICS | PRIMITIVE-IDEALS | REPRESENTATIONS | Skryabin's equivalence | NILPOTENT ORBITS | REDUCTIVE GROUPS | Algebra

Journal Article

Selecta Mathematica, ISSN 1022-1824, 4/2014, Volume 20, Issue 2, pp. 491 - 584

We construct a genus one analogue of the theory of associators and the Grothendieck–Teichmüller (GT) group. The analogue of the Galois action on the profinite...

Braid groups in genus one | 11M32 | Grothendieck–Teichmüller theory | Mathematics, general | 17B35 (16S30) | Mathematics | Moduli spaces of elliptic curves | 20F36 | Elliptic associators | 32G34 | Grothendieck-Teichmüller theory | MATHEMATICS | MATHEMATICS, APPLIED | MARKED CURVES | GALOIS REPRESENTATIONS | Grothendieck-Teichmuller theory | MODULAR-FORMS | Algebra

Braid groups in genus one | 11M32 | Grothendieck–Teichmüller theory | Mathematics, general | 17B35 (16S30) | Mathematics | Moduli spaces of elliptic curves | 20F36 | Elliptic associators | 32G34 | Grothendieck-Teichmüller theory | MATHEMATICS | MATHEMATICS, APPLIED | MARKED CURVES | GALOIS REPRESENTATIONS | Grothendieck-Teichmuller theory | MODULAR-FORMS | Algebra

Journal Article

Bulletin of the London Mathematical Society, ISSN 0024-6093, 06/2015, Volume 47, Issue 3, pp. 473 - 482

Abstract The McCool group, denoted $P\Sigma _n$, is the group of pure symmetric automorphisms of a free group of rank $n$. A presentation of the cohomology...

MATHEMATICS | SERIES

MATHEMATICS | SERIES

Journal Article

Mathematische Zeitschrift, ISSN 0025-5874, 12/2013, Volume 275, Issue 3, pp. 793 - 833

Let $$\mathbf{G}$$ be a connected split reductive group over a $$p$$ -adic field. In the first part of the paper we prove, under certain assumptions on...

22E50 | Mathematics, general | Mathematics | 11F85 | 16S30 | DISTRIBUTIONS | MATHEMATICS | REPRESENTATIONS | SEMISIMPLE LIE-ALGEBRA | ARITHMETIC D-MODULES | DIFFERENTIAL-OPERATORS | Algebra

22E50 | Mathematics, general | Mathematics | 11F85 | 16S30 | DISTRIBUTIONS | MATHEMATICS | REPRESENTATIONS | SEMISIMPLE LIE-ALGEBRA | ARITHMETIC D-MODULES | DIFFERENTIAL-OPERATORS | Algebra

Journal Article

Forum Mathematicum, ISSN 0933-7741, 07/2016, Volume 28, Issue 4, pp. 807 - 812

Let be a restricted Lie algebra over a field of characteristic and denote by its restricted enveloping algebra. We establish when the symmetric or skew...

Lie metabelian | polynomial identity | skew and symmetric elements | Restricted Lie algebra | 16R40 | 16S30 | 17B60 | enveloping algebra | 17B50 | 16W10 | MATHEMATICS | MATHEMATICS, APPLIED | INVOLUTION | GROUP-RINGS | Algebra | Lie groups

Lie metabelian | polynomial identity | skew and symmetric elements | Restricted Lie algebra | 16R40 | 16S30 | 17B60 | enveloping algebra | 17B50 | 16W10 | MATHEMATICS | MATHEMATICS, APPLIED | INVOLUTION | GROUP-RINGS | Algebra | Lie groups

Journal Article

Communications in Algebra, ISSN 0092-7872, 10/2015, Volume 43, Issue 10, pp. 4049 - 4053

The aim of this note is to communicate a simple example of a Lie-Rinehart algebra whose enveloping algebra is not a Hopf algebroid, neither in the sense of...

Hopf algebroids | Lie algebroids | Lie-Rinehart algebras | Lie–Rinehart algebras | MATHEMATICS | 57T05 | 16S30 | 16T05 | QUANTUM GROUPOIDS

Hopf algebroids | Lie algebroids | Lie-Rinehart algebras | Lie–Rinehart algebras | MATHEMATICS | 57T05 | 16S30 | 16T05 | QUANTUM GROUPOIDS

Journal Article

Algebras and Representation Theory, ISSN 1386-923X, 4/2014, Volume 17, Issue 2, pp. 675 - 701

In this paper we investigate a multi-parameter deformation $\mathfrak{B}_{r,s}^n(a,\lambda,\delta)$ of the walled Brauer algebra which was previously...

Mixed tensor space | 16D20 | Associative Rings and Algebras | Non-associative Rings and Algebras | 16S30 | Commutative Rings and Algebras | Schur–Weyl duality | Mathematics | 33D80 | 20C08 | 17B37 | Walled Brauer algebra | Schur-Weyl duality | MATHEMATICS | GENERAL LINEAR-GROUPS | REPRESENTATIONS | INVARIANT | HIGHEST WEIGHT CATEGORIES | Algebra

Mixed tensor space | 16D20 | Associative Rings and Algebras | Non-associative Rings and Algebras | 16S30 | Commutative Rings and Algebras | Schur–Weyl duality | Mathematics | 33D80 | 20C08 | 17B37 | Walled Brauer algebra | Schur-Weyl duality | MATHEMATICS | GENERAL LINEAR-GROUPS | REPRESENTATIONS | INVARIANT | HIGHEST WEIGHT CATEGORIES | Algebra

Journal Article

Letters in Mathematical Physics, ISSN 0377-9017, 11/2017, Volume 107, Issue 11, pp. 2047 - 2080

Following an idea of Nigel Higson, we develop a method for proving the existence of a meromorphic continuation for some spectral zeta functions. The method is...

Operator | Meromorphic continuation | Theoretical, Mathematical and Computational Physics | Complex Systems | 16S30 | Physics | Geometry | 22E25 | 17B35 | 46E35 | Zeta function | Group Theory and Generalizations | Nilpotent Lie algebra | 81R60 | ALGEBRAS | FORMULA | PHYSICS, MATHEMATICAL | OPERATORS | Algebra

Operator | Meromorphic continuation | Theoretical, Mathematical and Computational Physics | Complex Systems | 16S30 | Physics | Geometry | 22E25 | 17B35 | 46E35 | Zeta function | Group Theory and Generalizations | Nilpotent Lie algebra | 81R60 | ALGEBRAS | FORMULA | PHYSICS, MATHEMATICAL | OPERATORS | Algebra

Journal Article

Applied Categorical Structures, ISSN 0927-2852, 2/2015, Volume 23, Issue 1, pp. 93 - 105

We show that the functor from bialgebras to vector spaces sending a bialgebra to its subspace of primitives has monadic length at most 2.

Geometry | Monads | Convex and Discrete Geometry | Lie algebras | Secondary 16S30 | Mathematics | Theory of Computation | Primary 18C15 | Mathematical Logic and Foundations | MATHEMATICS | ALGEBRAS | RINGS | GALOIS CORINGS | COMATRIX CORINGS | Algebra

Geometry | Monads | Convex and Discrete Geometry | Lie algebras | Secondary 16S30 | Mathematics | Theory of Computation | Primary 18C15 | Mathematical Logic and Foundations | MATHEMATICS | ALGEBRAS | RINGS | GALOIS CORINGS | COMATRIX CORINGS | Algebra

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

Algebras and Representation Theory, ISSN 1386-923X, 8/2011, Volume 14, Issue 4, pp. 601 - 608

We study the problem of the existence of filtered multiplicative bases of a restricted enveloping algebra u(L), where L is a finite-dimensional and p-nilpotent...

Primary 16S30 | Restricted enveloping algebra | Associative Rings and Algebras | Non-associative Rings and Algebras | Filtered multiplicative basis | Commutative Rings and Algebras | Mathematics | 17B50 | LIE-ALGEBRAS | MATHEMATICS

Primary 16S30 | Restricted enveloping algebra | Associative Rings and Algebras | Non-associative Rings and Algebras | Filtered multiplicative basis | Commutative Rings and Algebras | Mathematics | 17B50 | LIE-ALGEBRAS | MATHEMATICS

Journal Article

Algebras and Representation Theory, ISSN 1386-923X, 2/2012, Volume 15, Issue 1, pp. 109 - 118

We define, over $k = {\Bbb{F}}_{p}$ , a splitting of the Frobenius morphism $Fr : {\text{Dist}}\,(G) \rightarrow {\text{Dist}}\,(G)$ on the whole...

Associative Rings and Algebras | Non-associative Rings and Algebras | 16S30 | Commutative Rings and Algebras | 14F10 | Mathematics | Algebra of distributions | 17B50 | Frobenius splitting

Associative Rings and Algebras | Non-associative Rings and Algebras | 16S30 | Commutative Rings and Algebras | 14F10 | Mathematics | Algebra of distributions | 17B50 | Frobenius splitting

Journal Article

Archiv der Mathematik, ISSN 0003-889X, 5/2005, Volume 84, Issue 5, pp. 398 - 405

We characterize the restricted Lie algebras L whose restricted universal enveloping algebra u(L) is Lie metabelian. Moreover, we show that the last condition...

Mathematics, general | Mathematics | 17B60 | 17B50 | 16S30 | MATHEMATICS

Mathematics, general | Mathematics | 17B60 | 17B50 | 16S30 | MATHEMATICS

Journal Article

Applied Mathematics-A Journal of Chinese Universities, ISSN 1005-1031, 3/2014, Volume 29, Issue 1, pp. 119 - 126

In this article, we consider endomorphism algebras of direct sums of some local left ideals over a local algebra and give a construction of quasi-hereditary...

quasi-hereditary algebra | 16S30 | Mathematics, general | Mathematics | local algebra | Applications of Mathematics | 16G10 | endomorphism algebra | MATHEMATICS, APPLIED

quasi-hereditary algebra | 16S30 | Mathematics, general | Mathematics | local algebra | Applications of Mathematics | 16G10 | endomorphism algebra | MATHEMATICS, APPLIED

Journal Article

Communications in Algebra, ISSN 0092-7872, 08/2011, Volume 39, Issue 8, pp. 2723 - 2751

In this article, the notion of universal enveloping algebra introduced in Ardizzoni [ 4 ] is specialized to the case of braided vector spaces whose Nichols...

Quadratic algebras | Braided bialgebras | Universal enveloping algebras | Nichols algebras | Secondary 16S30 | Braided Lie algebras | Computer algebra system | Primary 16W30 | Braided lie algebras | MATHEMATICS | POINTED HOPF-ALGEBRAS | Algebra | Vector spaces | Braiding | Classification | Lie groups

Quadratic algebras | Braided bialgebras | Universal enveloping algebras | Nichols algebras | Secondary 16S30 | Braided Lie algebras | Computer algebra system | Primary 16W30 | Braided lie algebras | MATHEMATICS | POINTED HOPF-ALGEBRAS | Algebra | Vector spaces | Braiding | Classification | Lie groups

Journal Article

Algebras and Representation Theory, ISSN 1386-923X, 12/2010, Volume 13, Issue 6, pp. 653 - 660

Let L be a non-abelian restricted Lie algebra over a field of characteristic p > 0 and let u(L) denote its restricted enveloping algebra. In Siciliano (Publ...

Associative Rings and Algebras | Restricted Lie algebra | Non-associative Rings and Algebras | Lie derived length | Enveloping algebra | 16S30 | Commutative Rings and Algebras | Mathematics | 17B60 | 17B50 | MATHEMATICS

Associative Rings and Algebras | Restricted Lie algebra | Non-associative Rings and Algebras | Lie derived length | Enveloping algebra | 16S30 | Commutative Rings and Algebras | Mathematics | 17B60 | 17B50 | MATHEMATICS

Journal Article

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