Lie algebra type noncommutative phase spaces are Hopf algebroids

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• 作者：Stjepan Meljanac ; Zoran Škoda ; Martina Stojić
• 关键词：Universal enveloping algebra ; Noncommutative phase space ; Deformed derivative ; Hopf algebroid ; Completed tensor product
• 刊名：Letters in Mathematical Physics
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：107
• 期：3
• 页码：475-503
• 全文大小：
• 刊物类别：Physics and Astronomy
• 刊物主题：Theoretical, Mathematical and Computational Physics; Complex Systems; Geometry; Group Theory and Generalizations;
• 出版者：Springer Netherlands
• ISSN：1573-0530
• 卷排序：107

文摘

For a noncommutative configuration space whose coordinate algebra is the universal enveloping algebra of a finite-dimensional Lie algebra, it is known how to introduce an extension playing the role of the corresponding noncommutative phase space, namely by adding the commuting deformed derivatives in a consistent and nontrivial way; therefore, obtaining certain deformed Heisenberg algebra. This algebra has been studied in physical contexts, mainly in the case of the kappa-Minkowski space-time. Here, we equip the entire phase space algebra with a coproduct, so that it becomes an instance of a completed variant of a Hopf algebroid over a noncommutative base, where the base is the enveloping algebra.