An extension of a q-deformed Heisenberg algebra and its Lie polynomials

被引：4
|
作者：
Cantuba, Rafael Reno S. [1 ]
Merciales, Mark Anthony C. [1 ]
机构：
[1] De La Salle Univ, Math & Stat Dept, Manila, Philippines
来源：
EXPOSITIONES MATHEMATICAE | 2021年 / 39卷 / 01期
关键词：
q-deformed Heisenberg algebra; Diamond lemma; Lie polynomial; Central extension; OSCILLATOR;
D O I：
10.1016/j.exmath.2019.12.001
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Let F be a field, and fix a q is an element of F. The q-deformed Heisenberg algebra H(q) is the unital associative algebra over F with generators A, B and a relation which asserts that AB - qB A is the multiplicative identity in H(q). We extend H(q) into an algebra R(q) defined by generators A, B and a relation which asserts that AB - qB A is central in R(q). We identify all elements of R(q) that are Lie polynomials in A, B. (C) 2020 Elsevier GmbH. All rights reserved.
引用
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页码：1 / 24
页数：24
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