Bicocycle double cross constructions

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Esen O., Guha P., Sütlü S.

Journal of Algebra and its Applications, cilt.22, sa.12, 2023 (SCI-Expanded, Scopus) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 22 Sayı: 12
  • Basım Tarihi: 2023
  • Doi Numarası: 10.1142/s0219498823502547
  • Dergi Adı: Journal of Algebra and its Applications
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Anahtar Kelimeler: 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
  • Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
  • Kocaeli Üniversitesi Adresli: Hayır

Özet

© 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.