Annihilator ideals of finite dimensional simple modules of two-parameter quantized enveloping algebra U r , s ( 𝔰𝔩 2 )

Yu Wang; Xiaoming Li

Czechoslovak Mathematical Journal (2023)

  • Volume: 73, Issue: 3, page 715-731
  • ISSN: 0011-4642

Abstract

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Let U be the two-parameter quantized enveloping algebra U r , s ( 𝔰𝔩 2 ) and F ( U ) the locally finite subalgebra of U under the adjoint action. The aim of this paper is to determine some ring-theoretical properties of F ( U ) in the case when r s - 1 is not a root of unity. Then we describe the annihilator ideals of finite dimensional simple modules of U by generators.

How to cite

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Wang, Yu, and Li, Xiaoming. "Annihilator ideals of finite dimensional simple modules of two-parameter quantized enveloping algebra $U_{r,s}(\mathfrak {sl}_2)$." Czechoslovak Mathematical Journal 73.3 (2023): 715-731. <http://eudml.org/doc/299101>.

@article{Wang2023,
abstract = {Let $U$ be the two-parameter quantized enveloping algebra $U_\{r,s\}(\mathfrak \{sl\}_2)$ and $F(U)$ the locally finite subalgebra of $U$ under the adjoint action. The aim of this paper is to determine some ring-theoretical properties of $F(U)$ in the case when $rs^\{-1\}$ is not a root of unity. Then we describe the annihilator ideals of finite dimensional simple modules of $U$ by generators.},
author = {Wang, Yu, Li, Xiaoming},
journal = {Czechoslovak Mathematical Journal},
keywords = {two-parameter quantum group; locally finite subalgebra; adjoint action; annihilator ideal},
language = {eng},
number = {3},
pages = {715-731},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Annihilator ideals of finite dimensional simple modules of two-parameter quantized enveloping algebra $U_\{r,s\}(\mathfrak \{sl\}_2)$},
url = {http://eudml.org/doc/299101},
volume = {73},
year = {2023},
}

TY - JOUR
AU - Wang, Yu
AU - Li, Xiaoming
TI - Annihilator ideals of finite dimensional simple modules of two-parameter quantized enveloping algebra $U_{r,s}(\mathfrak {sl}_2)$
JO - Czechoslovak Mathematical Journal
PY - 2023
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 73
IS - 3
SP - 715
EP - 731
AB - Let $U$ be the two-parameter quantized enveloping algebra $U_{r,s}(\mathfrak {sl}_2)$ and $F(U)$ the locally finite subalgebra of $U$ under the adjoint action. The aim of this paper is to determine some ring-theoretical properties of $F(U)$ in the case when $rs^{-1}$ is not a root of unity. Then we describe the annihilator ideals of finite dimensional simple modules of $U$ by generators.
LA - eng
KW - two-parameter quantum group; locally finite subalgebra; adjoint action; annihilator ideal
UR - http://eudml.org/doc/299101
ER -

References

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