scholarly journals A multiparameter family of irreducible representations of the quantum plane and of the quantum Weyl algebra

2015 ◽  
Vol 72 (4) ◽  
pp. 407-419
Author(s):  
Samuel Lopes ◽  
João Lourenço
Keyword(s):  
Weyl Algebra ◽  
Irreducible Representations ◽  
Quantum Plane ◽  
Quantum Weyl Algebra

Quantum Weyl Algebra

2004 ◽  
pp. 329-329
Author(s):  
Jian-zu Zhang ◽  
Roberto Floreanini ◽  
Steven Duplij ◽  
Steven Duplij ◽  
Dmitri Gitman ◽  
...  
Keyword(s):  
Weyl Algebra ◽  
Quantum Weyl Algebra

scholarly journals BGG CATEGORY FOR THE QUANTUM SCHRÖDINGER ALGEBRA

2020 ◽  
pp. 1-14
Author(s):  
GENQIANG LIU ◽  
YANG LI
Keyword(s):  
Complex Number ◽  
Full Subcategory ◽  
Weyl Algebra ◽  
Central Charge ◽  
Enveloping Algebra ◽  
Root Of Unity ◽  
Finite Dimensional ◽  
Quantum Weyl Algebra ◽  
Schrödinger Algebra

Abstract In 1996, a q-deformation of the universal enveloping algebra of the Schrödinger Lie algebra was introduced in Dobrev et al. [J. Phys. A 29 (1996) 5909–5918.]. This algebra is called the quantum Schrödinger algebra. In this paper, we study the Bernstein-Gelfand-Gelfand (BGG) category $\mathcal{O}$ for the quantum Schrödinger algebra $U_q(\mathfrak{s})$ , where q is a nonzero complex number which is not a root of unity. If the central charge $\dot z\neq 0$ , using the module $B_{\dot z}$ over the quantum Weyl algebra $H_q$ , we show that there is an equivalence between the full subcategory $\mathcal{O}[\dot Z]$ consisting of modules with the central charge $\dot z$ and the BGG category $\mathcal{O}^{(\mathfrak{sl}_2)}$ for the quantum group $U_q(\mathfrak{sl}_2)$ . In the case that $\dot z = 0$ , we study the subcategory $\mathcal{A}$ consisting of finite dimensional $U_q(\mathfrak{s})$ -modules of type 1 with zero action of Z. We directly construct an equivalence functor from $\mathcal{A}$ to the category of finite dimensional representations of an infinite quiver with some quadratic relations. As a corollary, we show that the category of finite dimensional $U_q(\mathfrak{s})$ -modules is wild.

The irreducible representations of the first weyl algebra

1992 ◽  
Vol 20 (5) ◽  
pp. 1493-1509
Author(s):  
Bruno J. Müller ◽  
ying-Lan Zhang
Keyword(s):  
Weyl Algebra ◽  
Irreducible Representations

Ap-Adic Quantum Weyl Algebra

2010 ◽  
Vol 38 (6) ◽  
pp. 2300-2310 ◽  
Author(s):  
Fana Tangara
Keyword(s):  
Weyl Algebra ◽  
Quantum Weyl Algebra

scholarly journals On the cohomology of the Weyl algebra, the quantum plane, and the q-Weyl algebra

2014 ◽  
Vol 218 (5) ◽  
pp. 879-887 ◽  
Author(s):  
Murray Gerstenhaber ◽  
Anthony Giaquinto
Keyword(s):  
Weyl Algebra ◽  
Quantum Plane

Fermionic and Bosonic Representations of the Extended Affine Lie Algebra

2002 ◽  
Vol 45 (4) ◽  
pp. 623-633 ◽  
Author(s):  
Yun Gao
Keyword(s):  
Lie Algebra ◽  
Weyl Algebra ◽  
Irreducible Representations ◽  
Affine Lie Algebra ◽  
Level 1 ◽  
Extended Affine Lie Algebra

AbstractWe construct a class of fermions (or bosons) by using a Clifford (or Weyl) algebra to get two families of irreducible representations for the extended affine Lie algebra of level (1, 0) (or (−1, 0)).

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