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Journal of Algebra, ISSN 0021-8693, 02/2015, Volume 424, pp. 506 - 521
For a simple module M over the positive part of the Virasoro algebra (actually for any simple module over some finite dimensional solvable Lie algebras ar) and... 
Virasoro algebra | Simple module | Weight module | MATHEMATICS | FINITE | LIE-ALGEBRA SL | CLASSIFICATION | WZW MODEL | IRREDUCIBLE REPRESENTATIONS | VECTORS | POSITIVE PART | Algebra
Journal Article
Journal of Algebra and its Applications, ISSN 0219-4988, 2016, Volume 16, Issue 5
In this paper, we construct and study some non-weight modules for the HeisenbergVirasoro algebra and the W algebra W(2, 2). We determine the modules, whose... 
simple modules | (Formula presented.) algebra (Formula presented.)(2,2) | Heisenberg–Virasoro algebra | MATHEMATICS | MATHEMATICS, APPLIED | REPRESENTATIONS | SPACES | W algebra W(2,2) | HARISH-CHANDRA MODULES | LIE-ALGEBRA | Heisenberg-Virasoro algebra | CLASSIFICATION | POSITIVE PART | FAMILY
Journal Article
Journal of Algebra, ISSN 0021-8693, 10/2015, Volume 440, pp. 245 - 263
For any finite-dimensional simple Lie algebra g and finitely generated commutative associative algebra S, we give a complete classification of the simple... 
Admissible representations | Infinite-dimensional Lie algebras | Weight modules | Current algebras | MATHEMATICS | REPRESENTATIONS | CLASSIFICATION | SIMPLE LIE-ALGEBRAS | Algebra
Journal Article
Journal of Algebra, ISSN 0021-8693, 06/2017, Volume 479, pp. 437 - 460
Using simple modules over the derivation Lie algebra C[t]ddt for the polynomial algebra C[t], we construct new weight modules over the Witt algebra where all... 
Isomorphism | Simple module | Weight module | Witt algebra | Weyl algebra | MATHEMATICS | FINITE | REPRESENTATIONS | LIE-ALGEBRA | CLASSIFICATION | WZW MODEL | POSITIVE PART | Information science | Algebra
Journal Article
Journal of Geometry and Physics, ISSN 0393-0440, 12/2018, Volume 134, pp. 11 - 18
In this paper, we study some non-weight modules over the loop-Virasoro algebra L and Block type Lie algebras B(q), where q is a nonzero complex number. Those... 
Loop-Virasoro algebra | Simple module | Non-weight module | Block type Lie algebra | Virasoro algebra | HARISH-CHANDRA MODULES | CLASSIFICATION | PHYSICS, MATHEMATICAL | FAMILY | LIE-ALGEBRAS | MATHEMATICS | IRREDUCIBLE MODULES | QUASIFINITE REPRESENTATIONS | Algebra
Journal Article
Canadian Mathematical Bulletin, ISSN 0008-4395, 03/2018, Volume 61, Issue 1, pp. 16 - 39
A classification of simple weight modules over the Schrodinger algebra is given. The Krull and the global dimensions are found for the centralizer C-s (H) (and... 
Krull dimension | Global dimension | Centralizer | Simple module | Tensor Krull minimal algebra | Weight module | Tensor homological minimal algebra | global dimension | REPRESENTATIONS | GENERALIZED WEYL ALGEBRAS | RINGS | tensor Krull minimal algebra | MATHEMATICS | FINITE | weight module | tensor homological minimal algebra | simple module | centralizer | ENVELOPING ALGEBRA
Journal Article
Journal of Algebra, ISSN 0021-8693, 02/2017, Volume 472, pp. 172 - 194
We study simple non-weight sl(2)-modules which are finitely generated as C[z]-modules. We show that they are described in terms of semilinear endomorphisms and... 
Non-weight modules | Simple modules | [formula omitted]-representations | sl-representations | MATHEMATICS | LIE-ALGEBRA SL | IRREDUCIBLE REPRESENTATIONS
Journal Article
Transformation Groups, ISSN 1083-4362, 9/2017, Volume 22, Issue 3, pp. 591 - 630
Characteristic cycles, leading term cycles, associated varieties and Harish-Chandra cells are computed for the family of highest weight Harish-Chandra modules... 
Topological Groups, Lie Groups | Mathematics | Algebra | LEADING-TERM CYCLES | MATHEMATICS | CLASSICAL-GROUPS | WEYL GROUPS | PRIMITIVE-IDEALS | REPRESENTATIONS | CHARACTERISTIC VARIETIES | ALGEBRA | SEMISIMPLE LIE-GROUPS | IRREDUCIBLE CHARACTERS | ANNIHILATORS
Journal Article
Proceedings of the American Mathematical Society, ISSN 0002-9939, 06/2018, Volume 146, Issue 6, pp. 2373 - 2380
For the algebra \mathbb{I}_1= K\langle x, \frac {d}{dx}, \int \rangle of polynomial integro-differential operators over a field K of characteristic zero, a... 
Simple module | Indecomposable module | The algebra of polynomial integro-differential operators | Generalized weight module | MATHEMATICS | MATHEMATICS, APPLIED | REPRESENTATIONS | generalized weight module | simple module | WEYL ALGEBRAS | indecomposable module
Journal Article
Journal of Algebra, ISSN 0021-8693, 02/2017, Volume 471, pp. 492 - 510
Let g be a finite-dimensional semisimple Lie algebra over C having rank l and let V be an irreducible finite-dimensional g-module having highest weight λ.... 
Irreducible modules | Freudenthal's formula | Verma modules | Weight multiplicities | Semisimple complex Lie algebras | BGG category | MATHEMATICS | FORMULA | Algebra | Algorithms
Journal Article
Journal of Pure and Applied Algebra, ISSN 0022-4049, 10/2014, Volume 218, Issue 10, pp. 1885 - 1899
We study irreducible representations of two classes of conformal Galilei algebras in 1-spatial dimension. We construct a functor which transforms simple... 
LIE-ALGEBRAS | MATHEMATICS | SIMPLE WEIGHT MODULES | MATHEMATICS, APPLIED | SYMMETRIES | DYNAMICAL REALIZATIONS | SCHRODINGER ALGEBRA | CLASSIFICATION | SL | Algebra | Mathematics | Naturvetenskap | Natural Sciences | Algebra and Logic | Algebra och logik | Matematik
Journal Article
Journal of Algebra, ISSN 0021-8693, 09/2013, Volume 390, pp. 77 - 86
We construct a large class of simple modules for the Heisenberg–Virasoro algebra. These modules are determined by the simple modules over the... 
Highest weight module | Whittaker module | Simple module | Heisenberg–Virasoro algebra | Heisenberg-Virasoro algebra | MATHEMATICS | WHITTAKER MODULES | LIE-ALGEBRA | VECTORS | Algebra
Journal Article
Journal of Pure and Applied Algebra, ISSN 0022-4049, 07/2015, Volume 219, Issue 7, pp. 2799 - 2815
It is proved that a simple module which is locally finite over the positive part of the Cartan decomposition for a finite-dimensional Lie algebra with... 
MATHEMATICS | SIMPLE WEIGHT MODULES | MATHEMATICS, APPLIED | CLASSIFICATION | WHITTAKER MODULES | IRREDUCIBLE REPRESENTATIONS | Algebra
Journal Article
Journal of Noncommutative Geometry, ISSN 1661-6952, 2018, Volume 12, Issue 3, pp. 889 - 946
Journal Article
Communications in Algebra, ISSN 0092-7872, 04/2018, Volume 46, Issue 4, pp. 1770 - 1798
Journal Article
Communications in Algebra, ISSN 0092-7872, 10/2017, Volume 45, Issue 10, pp. 4166 - 4189
Various classes of simple torsion modules are classified over the quantum spatial ageing algebra (this is a Noetherian algebra of Gelfand-Kirillov dimension... 
a graded module | an Ore set | weight module | torsion module | the quantum spatial ageing algebra | simple module | centralizer | A denominator set | a graded algebra | MATHEMATICS | REPRESENTATIONS | JORDAN PLANE | Aging | Algebra | Torsion | Modules
Journal Article
Journal of Algebra, ISSN 0021-8693, 2007, Volume 307, Issue 1, pp. 209 - 214
We show that the support of a simple weight module over the Virasoro algebra, which has an infinite-dimensional weight space, coincides with the weight lattice... 
Simple module | Weight module | Virasoro algebra | Support | MATHEMATICS | weight module | REPRESENTATIONS | simple module | LIE-ALGEBRA | support | Naturvetenskap | Mathematics | Natural Sciences | Matematik
Journal Article
Linear Algebra and Its Applications, ISSN 0024-3795, 06/2015, Volume 475, pp. 276 - 291
Generalized Heisenberg algebras H(f) for any polynomial f(h)∈C[h] have been used to explain various physical systems and many physical phenomena for the last... 
Isomorphism | Simple module | Generalized Heisenberg algebra | Weight module | MATHEMATICS | MATHEMATICS, APPLIED | LIPKIN MODEL | SPECTRUM | Algebra
Journal Article
Advances in Mathematics, ISSN 0001-8708, 2006, Volume 206, Issue 2, pp. 630 - 656
Let G be a rank n additive subgroup of C and Vir [ G ] the corresponding Virasoro algebra of rank n. In the present paper, irreducible weight modules with... 
Virasoro algebra | Generalized Virasoro algebra | Weight module | MATHEMATICS | GENERALIZED WITT ALGEBRAS | weight module | VERMA MODULES | HARISH-CHANDRA MODULES | generalized Virasoro algebra | SIMPLE LIE-ALGEBRAS
Journal Article
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