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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
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
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
Journal Article
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
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
Journal Article
by Gao, F
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
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
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
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
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
Journal Article
Algebras and Representation Theory, ISSN 1386-923X, 12/2014, Volume 17, Issue 6, pp. 1843 - 1852
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
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
Journal Article
Journal of Operator Theory, ISSN 0379-4024, 03/2017, Volume 77, Issue 2, pp. 481 - 501
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
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
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
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
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
Journal Article
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