scholarly journals The Universal Enveloping Algebra of the Schrödinger Algebra and its Prime Spectrum

2018 ◽  
Vol 61 (4) ◽  
pp. 688-703 ◽  
Author(s):  
V. V. Bavula ◽  
T. Lu
Keyword(s):  
Universal Enveloping Algebra ◽  
Prime Spectrum ◽  
Enveloping Algebra ◽  
Whittaker Modules ◽  
Schrödinger Algebra

AbstractThe prime, completely prime, maximal, and primitive spectra are classified for the universal enveloping algebra of the Schrödinger algebra. The explicit generators are given for all of these ideals. A counterexample is constructed to the conjecture of Cheng and Zhang about nonexistence of simple singular Whittaker modules for the Schrödinger algebra (and all such modules are classified). It is proved that the conjecture holds ‘generically’.

scholarly journals PRIME SPECTRA OF AMBISKEW POLYNOMIAL RINGS

2018 ◽  
Vol 61 (1) ◽  
pp. 49-68
Author(s):  
CHRISTOPHER D. FISH ◽  
DAVID A. JORDAN
Keyword(s):  
Positive Integer ◽  
Polynomial Algebra ◽  
Central Element ◽  
Universal Enveloping Algebra ◽  
Polynomial Rings ◽  
Prime Ideals ◽  
Closed Field ◽  
Prime Spectrum ◽  
Enveloping Algebra ◽  
Root Of Unity

AbstractWe determine sufficient criteria for the prime spectrum of an ambiskew polynomial algebra R over an algebraically closed field 𝕂 to be akin to those of two of the principal examples of such an algebra, namely the universal enveloping algebra U(sl2) (in characteristic 0) and its quantization Uq(sl2) (when q is not a root of unity). More precisely, we determine sufficient criteria for the prime spectrum of R to consist of 0, the ideals (z − λ)R for some central element z of R and all λ ∈ 𝕂, and, for some positive integer d and each positive integer m, d height two prime ideals P for which R/P has Goldie rank m.

scholarly journals The prime spectrum of the universal enveloping algebra of the 1-spatial ageing algebra and of U(gl2)

2021 ◽  
Vol 31 (1) ◽  
pp. 1-16
Author(s):  
Volodymyr Bavula ◽  
◽  
Tao Lu ◽  
Keyword(s):  
Prime Ideal ◽  
Universal Enveloping Algebra ◽  
Explicit Description ◽  
Prime Spectrum ◽  
Enveloping Algebra

For the algebras in the title, their prime, primitive and maximal spectra are explicitly described. For each prime ideal an explicit set of generators is given. An explicit description of all the containments between primes is obtained.

scholarly journals Classification of Simple Weight Modules over the Schrödinger Algebra

2018 ◽  
Vol 61 (1) ◽  
pp. 16-39 ◽  
Author(s):  
V. V. Bavula ◽  
T. Lu
Keyword(s):  
Lie Algebra ◽  
Prime Factor ◽  
Universal Enveloping Algebra ◽  
Enveloping Algebra ◽  
Schrödinger Algebra ◽  
Weight Modules

AbstractA classification of simple weight modules over the Schrödinger algebra is given. The Krull and the global dimensions are found for the centralizer (H) (and some of its prime factor algebras) of the Cartan element H in the universal enveloping algebra of the Schrödinger (Lie) algebra. The simple (H)-modules are classified. The Krull and the global dimensions are found for some (prime) factor algebras of the algebra (over the centre). It is proved that some (prime) factor algebras of and (H) are tensor homological/Krull minimal.

scholarly journals DG Poisson algebra and its universal enveloping algebra

2016 ◽  
Vol 59 (5) ◽  
pp. 849-860 ◽  
Author(s):  
JiaFeng Lü ◽  
XingTing Wang ◽  
GuangBin Zhuang
Keyword(s):  
Poisson Algebra ◽  
Universal Enveloping Algebra ◽  
Enveloping Algebra

scholarly journals Quasi-Whittaker modules for the Schrödinger algebra

2014 ◽  
Vol 463 ◽  
pp. 16-32 ◽  
Author(s):  
Yan-an Cai ◽  
Yongsheng Cheng ◽  
Ran Shen
Keyword(s):  
Whittaker Modules ◽  
Schrödinger Algebra

scholarly journals ELEMENTARY INVARIANTS FOR CENTRALIZERS OF NILPOTENT MATRICES

2009 ◽  
Vol 86 (1) ◽  
pp. 1-15 ◽  
Author(s):  
JONATHAN BROWN ◽  
JONATHAN BRUNDAN
Keyword(s):  
Lie Algebra ◽  
Characteristic Zero ◽  
Universal Enveloping Algebra ◽  
General Linear ◽  
Enveloping Algebra ◽  
Nilpotent Matrix ◽  
Nilpotent Matrices ◽  
Algebra Over A Field

AbstractWe construct an explicit set of algebraically independent generators for the center of the universal enveloping algebra of the centralizer of a nilpotent matrix in the general linear Lie algebra over a field of characteristic zero. In particular, this gives a new proof of the freeness of the center, a result first proved by Panyushev, Premet and Yakimova.

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