Twisted Traces and Positive Forms on Generalized q-Weyl Algebras

被引：1

作者：

Klyuev, Daniil ^{[1
]}

机构：

[1] MIT, Dept Math, Cambridge, MA 02139 USA

来源：

SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS | 2022年 / 18卷

关键词：

quantization; trace; inner product; star-product;

D O I：

10.3842/SIGMA.2022.009

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let A be a generalized q-Weyl algebra, it is generated by u, v, Z, Z(-1) with relations ZuZ(-1) = q(2)u, ZvZ(-1) = q(-2)v, uv = P(q(-1)Z), vu = P(qZ), where P is a Laurent polynomial. A Hermitian form (.,.) on A is called invariant if (Za, b) = (a, bZ(-1)), (ua, b) = (a, sbv), (va, b) = (a, s(-1)bu) for some s is an element of C with |s| = 1 and all a, b is an element of A. In this paper we classify positive definite invariant Hermitian forms on generalized q-Weyl algebras.

引用

页数：28

共 11 条

[1]

Bavula V. V., 1993, St. Petersburg Math. J, V4, P71

[2] Deformation Quantization and Superconformal Symmetry in Three Dimensions [J].