Star-products for Lie-algebraic noncommutative Minkowski space-times

Maris, Valentine; Požar, filip; Wallet, Jean-Christophe (2025) Star-products for Lie-algebraic noncommutative Minkowski space-times. Journal of High Energy Physics, 2025 (10). ISSN 1029-8479

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Abstract

Poisson structures of the Poincar & eacute; group can be linked to deformations of the Minkowski space-time, classified some time ago by Zakrewski. Based on this classification, various quantum Minkowski space-times with coordinates Lie algebras and specific Poincare Hopf algebras have been exhibited by Mercati and called T-Minkowski space-times". Here we construct the star products and involutions characterizing the star-algebras for a broad family of Lie algebras which includes 11 out of 17 Lie algebras of T-Minkowski spaces. We show that the usual Lebesgue integral defines either a trace or a KMS weight ("twisted trace") depending on whether the Lie group of the coordinates' Lie algebra is unimodular or not. Finally, we give the Poincar & eacute; Hopf algebras when they are compatible with our & lowast;-product. General derivation of such symmetry Hopf algebras are briefly discussed.

Item Type:	Article
Uncontrolled Keywords:	Non-Commutative Geometry; Quantum Groups
Subjects:	NATURAL SCIENCES > Physics NATURAL SCIENCES > Physics > Physics of Elementary Particles and Fields
Divisions:	Theoretical Physics Division
Depositing User:	Ema Buhin Šaler
Date Deposited:	03 Mar 2026 10:14
URI:	http://fulir.irb.hr/id/eprint/11295
DOI:	10.1007/jhep10(2025)002

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