Bicocycle double cross constructions

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Esen O., Guha P., Sütlü S.

Journal of Algebra and its Applications, vol.22, no.12, 2023 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 22 Issue: 12
  • Publication Date: 2023
  • Doi Number: 10.1142/s0219498823502547
  • Journal Name: Journal of Algebra and its Applications
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Keywords: Unified product, double cross product Lie groups, double cross sum Lie algebras, double cross product bialgebras, MATCHED PAIRS, HOPF-ALGEBRAS, EXTENDING STRUCTURES, PRODUCT BIALGEBRAS, LIE-GROUPS
  • Kocaeli University Affiliated: No

Abstract

© 2023 World Scientific Publishing Company.We introduce the notion of a bicocycle double cross product (sum) Lie group (algebra), and a bicocycle double cross product bialgebra, generalizing the unified products. On the level of Lie groups the construction yields a Lie group on the product space of two pointed manifolds, none of which being necessarily a subgroup. On the level of Lie algebras, a Lie algebra is obtained on the direct sum of two vector spaces, which are not required to be subalgebras. Finally, on the quantum level a bialgebra is obtained on the tensor product of two (co)algebras that are not necessarily sub-bialgebras.