Ur, t在量子平面上的模代数结构

Acta mathematica scientia,Series A ›› 2014, Vol. 34 ›› Issue (3): 540-561.

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U_{r, t}-module Algebra Structures on the Quantum Plane

HONG Yan-Yong^1,2, WU Zhi-Xiang²

1.College of Science, |Zhejiang Agriculture and Forestry University, |Hangzhou 311300|
2.Department of Mathematics, Zhejiang University, Hangzhou 310027

Received:2012-07-28 Revised:2013-10-15 Online:2014-06-25 Published:2014-06-25
Supported by:
国家自然科学基金(11171296)资助

Abstract

Abstract:

When q is not the root of unity and the ground field is C, we give a complete list of Ur_{, t}-module algebra structures on the quantum plane and describe these representations. Moreover, it is interesting to find that, in some cases, C_q[x, y]=\bigoplus\limits^∞_n=0C_q[x, y]_n, where C_q[x, y]_n is the n-th homogeneous component and is isomorphic to the irreducible representation V_{1, n, γ1^n/2} for some γ_1≠0.

Key words: Hopf algebra, Quantum plane, Module algebra structure, Verma module

CLC Number:

60W30

HONG Yan-Yong, WU Zhi-Xiang. U_{r, t}-module Algebra Structures on the Quantum Plane[J].Acta mathematica scientia,Series A, 2014, 34(3): 540-561.

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U_{r, t}-module Algebra Structures on the Quantum Plane

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U_{r, t}-module Algebra Structures on the Quantum Plane