Hopf-Sikorski algebras

• Autorzy: Heller M. , Odrzygóźdź Z. , Pysiak L. , Sasin W.
• Języki publikacji: EN

Abstrakty

EN

The dual category with respect to the category of differential groups is defined and investigated. The objects of this category are algebras, called Hopf-Sikorski (H-S) algebras, the axioms of which combine the axioms of Sikorski's algebras with modified axiomas of Hopf algebras. Morphisms of this category are structural mappings corresponding to Hopf algebras that are smooth in the sense of Sikorski. As an example, we discuss the H-S algebra of the Lorentz group.

Słowa kluczowe

EN

Hopf algebras; differential spaces; differential groups

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2011
• Tom: Vol. 44, nr 2
• Strony: 213--221
• Opis fizyczny: Bibliogr. 7 poz.

Twórcy

autor

Heller M.

• Ul. Powstańców Warszawy 13/94 33 110 Tarnów, Poland

autor

Odrzygóźdź Z.

• Department of Mathematics and Information Science Warsaw University of Technology Plac Politechniki 1 00 661 Warsaw, Poland

autor

Pysiak L.

• Department of Mathematics and Information Science Warsaw University of Technology Plac Politechniki 1 00 661 Warsaw, Poland

autor

Sasin W.

• Department of Mathematics and Information Science Warsaw University of Technology Plac Politechniki 1 00 661 Warsaw, Poland

Bibliografia

• [1] S.Majid, Foundations of Quantum Group Theory Cambridge University Press, Cambridge, 1995.
• [2] J.Nestruev, Smooth Manifolds and Observables, Graduate Texts in Mathematics, Vol. 220, Springer, 2002.
• [3] P.Multarzyński, Z.Pasternak-Winiarski, Differential groups and their Lie algebra, Demonstratio Math. 24 (2001), 515–537.
• [4] Z.Pasternak-Winiarski, Differential groups of class D0 and standard charts, Demonstratio Math. 16 (1981), 503–517.
• [5] R.Sikorski, Abstract covariant derivative, Colloq. Math. 18 (1967), 252–272.
• [6] R.Sikorski, Differential modules, Colloq. Math. 24 (1971), 45–70.
• [7] K.Spallek, Zur Klassifikacion differenzierbaren Gruppen, Manuscripta Math. 11 (1974), 345–357.