Journal of Algebra, ISSN 0021-8693, 09/2019, Volume 534, pp. 228 - 244

Let k be a field and let R be a left noetherian k-algebra. The algebra R satisfies the Dixmier-Moeglin equivalence if the annihilators of irreducible...

Morita equivalence | Dixmier-Moeglin equivalence | Prime spectrum | Tensor products | Primitive ideals | Idempotents | MATHEMATICS | ALGEBRAS | PRIMITIVE-IDEALS

Morita equivalence | Dixmier-Moeglin equivalence | Prime spectrum | Tensor products | Primitive ideals | Idempotents | MATHEMATICS | ALGEBRAS | PRIMITIVE-IDEALS

Journal Article

Representation Theory of the American Mathematical Society, ISSN 1088-4165, 11/2018, Volume 22, Issue 8, pp. 223 - 245

Let \frak g be a simple finite-dimensional Lie algebra over an algebraically closed field \mathbb{F} of characteristic 0. We denote by \mathrm {U}(\frak g) the...

W-algebras | Zigzag algebras | Self-injective modules | Primitive ideals | MATHEMATICS | SLICES | self-injective modules | MODULES | PRIMITIVE-IDEALS | ENVELOPING-ALGEBRAS | VARIETIES | CLASSIFICATION | SEMISIMPLE LIE-ALGEBRA | zigzag algebras

W-algebras | Zigzag algebras | Self-injective modules | Primitive ideals | MATHEMATICS | SLICES | self-injective modules | MODULES | PRIMITIVE-IDEALS | ENVELOPING-ALGEBRAS | VARIETIES | CLASSIFICATION | SEMISIMPLE LIE-ALGEBRA | zigzag algebras

Journal Article

Communications in Algebra, ISSN 0092-7872, 04/2017, Volume 45, Issue 4, pp. 1479 - 1482

We construct affine algebras with an arbitrary number of simple modules of each finite dimension.

simple modules | Primitive ideals | MATHEMATICS | Modules | Algebra | Mathematical analysis

simple modules | Primitive ideals | MATHEMATICS | Modules | Algebra | Mathematical analysis

Journal Article

4.
The prime spectrum of the algebra Kq[X,Y] ⋊ Uq(sl2) and a classification of simple weight modules

Journal of Noncommutative Geometry, ISSN 1661-6952, 2018, Volume 12, Issue 3, pp. 889 - 946

Journal Article

Journal of Algebra and its Applications, ISSN 0219-4988, 12/2015, Volume 14, Issue 10

For a special class of generalized Weyl algebras (GWAs), we prove a Duflo theorem stating that the annihilator of any simple module is in fact the annihilator...

Generalized Weyl algebras | primitive ideals | Duflo theorem | MATHEMATICS | MATHEMATICS, APPLIED | WEIGHT MODULES | PRIMITIVE-IDEALS | CLASSIFICATION | ENVELOPING ALGEBRA

Generalized Weyl algebras | primitive ideals | Duflo theorem | MATHEMATICS | MATHEMATICS, APPLIED | WEIGHT MODULES | PRIMITIVE-IDEALS | CLASSIFICATION | ENVELOPING ALGEBRA

Journal Article

Journal of the European Mathematical Society, ISSN 1435-9855, 2017, Volume 19, Issue 7, pp. 2019 - 2049

Brown and Gordon asked whether the Poisson Dixmier-Moeglin equivalence holds for any complex affine Poisson algebra, that is, whether the sets of Poisson...

Primitive ideal | Dixmier-Moeglin equivalence | Differential algebraic geometry | Poisson algebra | Manin kernel | Model theory | MATHEMATICS | MATHEMATICS, APPLIED | model theory | PRIME | PRIMITIVE-IDEALS | EXTENSIONS | differential algebraic geometry | primitive ideal

Primitive ideal | Dixmier-Moeglin equivalence | Differential algebraic geometry | Poisson algebra | Manin kernel | Model theory | MATHEMATICS | MATHEMATICS, APPLIED | model theory | PRIME | PRIMITIVE-IDEALS | EXTENSIONS | differential algebraic geometry | primitive ideal

Journal Article

MATHEMATISCHE ANNALEN, ISSN 0025-5831, 02/2020, Volume 376, Issue 1-2, pp. 289 - 358

We prove a formula for the dimension of Whittaker functionals of irreducible constituents of a regular unramified genuine principal series for covering groups....

SUPERCUSPIDAL REPRESENTATIONS | ORBITAL INTEGRALS | PRIMITIVE-IDEALS | Primary 11F70 | FINITE CENTRAL EXTENSIONS | CONJECTURE | CHARACTERS | Secondary 22E50 | MATHEMATICS | STANDARD MODULES | UNRAMIFIED REPRESENTATIONS | COEFFICIENTS | 20C08 | LANGLANDS QUOTIENT THEOREM

SUPERCUSPIDAL REPRESENTATIONS | ORBITAL INTEGRALS | PRIMITIVE-IDEALS | Primary 11F70 | FINITE CENTRAL EXTENSIONS | CONJECTURE | CHARACTERS | Secondary 22E50 | MATHEMATICS | STANDARD MODULES | UNRAMIFIED REPRESENTATIONS | COEFFICIENTS | 20C08 | LANGLANDS QUOTIENT THEOREM

Journal Article

Memoirs of the American Mathematical Society, ISSN 0065-9266, 05/2017, Volume 247, Issue 1169, pp. 1 - 134

All algebras in a very large, axiomatically defined class of quantum nilpotent algebras are proved to possess quantum cluster algebra structures under mild...

noncommutative unique factorization domains | SCHUBERT CELLS | CATENARITY | quantum nilpotent algebras | PRIMITIVE-IDEALS | iterated Ore extensions | RINGS | Quantum cluster algebras | MATHEMATICS | PRIME | UNIQUE FACTORIZATION DOMAINS | QUANTIZED WEYL ALGEBRAS | SPECTRA

noncommutative unique factorization domains | SCHUBERT CELLS | CATENARITY | quantum nilpotent algebras | PRIMITIVE-IDEALS | iterated Ore extensions | RINGS | Quantum cluster algebras | MATHEMATICS | PRIME | UNIQUE FACTORIZATION DOMAINS | QUANTIZED WEYL ALGEBRAS | SPECTRA

Journal Article

Advances in Mathematics, ISSN 0001-8708, 2006, Volume 200, Issue 1, pp. 136 - 195

We give a presentation for the finite W -algebra associated to a nilpotent matrix in the general linear Lie algebra over C . In the special case that the...

Finite W-algebras | Yangians | MATHEMATICS | PRIMITIVE-IDEALS | finite W-algebras | Business presentations

Finite W-algebras | Yangians | MATHEMATICS | PRIMITIVE-IDEALS | finite W-algebras | Business presentations

Journal Article

Mathematische Zeitschrift, ISSN 0025-5874, 2/2013, Volume 273, Issue 1, pp. 123 - 160

We consider finite W-algebras $${U(\mathfrak{g},e)}$$ associated to even multiplicity nilpotent elements in classical Lie algebras. We give a classification of...

Mathematics, general | 81R05 | Mathematics | 17B10 | MATHEMATICS | SLICES | PRIMITIVE-IDEALS | YANGIANS | Algebra

Mathematics, general | 81R05 | Mathematics | 17B10 | MATHEMATICS | SLICES | PRIMITIVE-IDEALS | YANGIANS | Algebra

Journal Article

Journal of Algebra, ISSN 0021-8693, 03/2016, Volume 450, pp. 458 - 486

Using the E-algebraic branching systems, various graded irreducible representations of a Leavitt path K-algebra L of a directed graph E are constructed. The...

Graded modules | Graded irreducible representations | Leavitt path algebras | Graded self-injective modules | Arbitrary graphs | Primitive ideals | Finitely presented graded simple modules | MATHEMATICS | SOCLE | SIMPLE MODULES | Algebra

Graded modules | Graded irreducible representations | Leavitt path algebras | Graded self-injective modules | Arbitrary graphs | Primitive ideals | Finitely presented graded simple modules | MATHEMATICS | SOCLE | SIMPLE MODULES | 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

Journal of Algebra, ISSN 0021-8693, 06/2012, Volume 359, pp. 80 - 88

In this note we classify the primitive ideals in finite W-algebras of type A.

W-algebras | Primitive ideals | MATHEMATICS | REPRESENTATIONS

W-algebras | Primitive ideals | MATHEMATICS | REPRESENTATIONS

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

Journal of Operator Theory, ISSN 0379-4024, 03/2017, Volume 77, Issue 2, pp. 481 - 501

We study the essential spectrum and Fredholm properties of certain integral and pseudo-differential operators associated to non-commutative locally compact...

algebra | Dynamical system | Fredholm operator | Pseudo-differential operator | Locally compact group | Essential spectrum | PRIMITIVE-IDEALS | pseudo-differential operator | EFFROS-HAHN CONJECTURE | C-ASTERISK-ALGEBRAS | PSEUDODIFFERENTIAL-OPERATORS | dynamical system | INFINITY | SPACE | MATHEMATICS | essential spectrum | STAR-ALGEBRAS | QUANTUM HAMILTONIANS | C-algebra | SCHRODINGER-OPERATORS

algebra | Dynamical system | Fredholm operator | Pseudo-differential operator | Locally compact group | Essential spectrum | PRIMITIVE-IDEALS | pseudo-differential operator | EFFROS-HAHN CONJECTURE | C-ASTERISK-ALGEBRAS | PSEUDODIFFERENTIAL-OPERATORS | dynamical system | INFINITY | SPACE | MATHEMATICS | essential spectrum | STAR-ALGEBRAS | QUANTUM HAMILTONIANS | C-algebra | SCHRODINGER-OPERATORS

Journal Article

Algebras and Representation Theory, ISSN 1386-923X, 4/2016, Volume 19, Issue 2, pp. 255 - 276

We consider the Deaconu–Renault groupoid of an action of a finitely generated free abelian monoid by local homeomorphisms of a locally compact Hausdorff space....

Primitive ideal | Associative Rings and Algebras | Groupoid | Irreducible representation | Non-associative Rings and Algebras | Primary 46L05 | C ∗ -algebra | Commutative Rings and Algebras | Mathematics | Secondary 46L45 | algebra

Primitive ideal | Associative Rings and Algebras | Groupoid | Irreducible representation | Non-associative Rings and Algebras | Primary 46L05 | C ∗ -algebra | Commutative Rings and Algebras | Mathematics | Secondary 46L45 | algebra

Journal Article

Advances in Mathematics, ISSN 0001-8708, 06/2019, Volume 349, pp. 459 - 487

Let G be a semiabelian variety defined over a field of characteristic 0, endowed with an endomorphism Φ. We prove there is no proper subvariety Y⊂G which...

Periodic subvarieties | Primitive ideals | Algebraic dynamics | DYNAMICAL BOGOMOLOV CONJECTURE | MATHEMATICS | MANIN-MUMFORD CONJECTURE | PRIMITIVE-IDEALS | EXTENSIONS | ENDOMORPHISMS

Periodic subvarieties | Primitive ideals | Algebraic dynamics | DYNAMICAL BOGOMOLOV CONJECTURE | MATHEMATICS | MANIN-MUMFORD CONJECTURE | PRIMITIVE-IDEALS | EXTENSIONS | ENDOMORPHISMS

Journal Article

Forum Mathematicum, ISSN 0933-7741, 05/2014, Volume 26, Issue 3, pp. 703 - 721

The aim of this paper is to study the representation theory of quantum Schubert cells. Let be a simple complex Lie algebra. To each element of the Weyl group...

20G42 | 17B22 | 16T20 | 17B37 | quantum Schubert cells | Primitive ideals | Quantum Schubert cells | MATHEMATICS | MATHEMATICS, APPLIED | ALGEBRAS | PRIME SPECTRA | H-STRATA | ENUMERATION

20G42 | 17B22 | 16T20 | 17B37 | quantum Schubert cells | Primitive ideals | Quantum Schubert cells | MATHEMATICS | MATHEMATICS, APPLIED | ALGEBRAS | PRIME SPECTRA | H-STRATA | ENUMERATION

Journal Article

Journal of Algebra, ISSN 0021-8693, 12/2013, Volume 396, pp. 184 - 206

We determine when a generalized down–up algebra is a Noetherian unique factorisation domain or a Noetherian unique factorisation ring.

Generalized down–up algebra | Noetherian unique factorisation domain | Noetherian unique factorisation ring | Generalized down-up algebra | MATHEMATICS | MODULES | PRIMITIVE-IDEALS | PRIME IDEALS | ENVELOPING ALGEBRA | POLYNOMIAL-RINGS | Algebra

Generalized down–up algebra | Noetherian unique factorisation domain | Noetherian unique factorisation ring | Generalized down-up algebra | MATHEMATICS | MODULES | PRIMITIVE-IDEALS | PRIME IDEALS | ENVELOPING ALGEBRA | POLYNOMIAL-RINGS | Algebra

Journal Article

Filomat, ISSN 0354-5180, 1/2017, Volume 31, Issue 7, pp. 2053 - 2060

This study is an attempt to prove the following main results. Let 𝒜 be a Banach algebra and 𝔄 = 𝒜 ⊕ ℂ be its unitization. By Π (𝔄), we denote the set of...

Integers | Commutativity | Algebra | Mathematical theorems | Logical proofs | Applied mathematics | Quotients | Subalgebras | Linear transformations | Primitive ideal | Banach algebra | Banach ∗-algebra | Socle | Spectrum | MATHEMATICS | MATHEMATICS, APPLIED | spectrum | primitive ideal | socle | Banach-algebra | DERIVATIONS

Integers | Commutativity | Algebra | Mathematical theorems | Logical proofs | Applied mathematics | Quotients | Subalgebras | Linear transformations | Primitive ideal | Banach algebra | Banach ∗-algebra | Socle | Spectrum | MATHEMATICS | MATHEMATICS, APPLIED | spectrum | primitive ideal | socle | Banach-algebra | DERIVATIONS

Journal Article

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