GELFAND-KIRILLOV DIMENSION OF THE QUANTIZED ALGEBRA OF REGULAR FUNCTIONS ON HOMOGENEOUS SPACES

被引：0

作者：

Chakraborty, Partha Sarathi ^{[1
,2
]}

Saurabh, Bipul ^{[3
]}

机构：

[1] Indian Stat Inst, Theoret Stat & Math Unit, 203 BT Rd, Kolkata 700010, India

[2] Inst Math Sci HBNI, CIT Campus, Chennai 600113, Tamil Nadu, India

[3] Indian Inst Technol, Palaj 382355, Gandhinagar, India

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2019年 / 147卷 / 08期

关键词：

Quantized function algebra; Weyl group; Gelfand-Kirillov dimension; QUANTUM; GROWTH;

D O I：

10.1090/proc/14522

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this article, we prove that the Gelfand-Kirillov dimension of the quantized algebra of regular functions on certain homogeneous spaces of types A, C, and D is equal to the dimension of the homogeneous space as a real differentiable manifold.

引用

页码：3289 / 3302

页数：14

共 16 条

[1]

BANICA T, 1999, EXPOSITION MATH, V17, P313

[2] GROWTH ESTIMATES FOR DISCRETE QUANTUM GROUPS [J].

Banica, Teodor ;

Vergnioux, Roland .

INFINITE DIMENSIONAL ANALYSIS QUANTUM PROBABILITY AND RELATED TOPICS, 2009, 12 (02) :321-340

[3] Ergodic coactions with large multiplicity and monoidal equivalence of quantum groups [J].

Bichon, J ;

De Rijdt, A ;

Vaes, S .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2006, 262 (03) :703-728

[4]

Bueso JL, 1998, LECT NOTES PURE APPL, V197, P55

[5] Gelfand-Kirillov dimension of some simple unitarizable modules [J].

Chakraborty, Partha Sarathi ;

Saurabh, Bipul .

JOURNAL OF ALGEBRA, 2018, 514 :199-218

[6] POLYNOMIAL GROWTH OF DISCRETE QUANTUM GROUPS, TOPOLOGICAL DIMENSION OF THE DUAL AND *-REGULARITY OF THE FOURIER ALGEBRA [J].

D'Andrea, Alessandro ;

Pinzari, Claudia ;

Rossi, Stefano .

ANNALES DE L INSTITUT FOURIER, 2017, 67 (05) :2003-2027

[7]

Gelfand I.M., 1966, Publications Mathmatiques de lIHS, P5, DOI [10.1007/BF02684800, DOI 10.1007/BF02684800]

[8]

Humphreys James E., 1990, CAMBRIDGE STUDIES AD, V29

[9]

Klimyk A., 1997, Quantum groups and their representations

[10]

KOROGODSKI LI, 1998, MATH SURVEYS MONOGRA, V0056

← 1 2 →