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Quantum families of quantum group homomorphisms.

Authors :
Budziński, Mariusz
Kasprzak, Paweł
Source :
Communications in Algebra; 2017, Vol. 45 Issue 4, p1627-1638, 12p
Publication Year :
2017

Abstract

The notion of a quantum family of maps has been introduced in the framework ofC -algebras. As in the classical case, one may consider a quantum family of maps preserving additional structures (e.g. quantum family of maps preserving a state). In this paper, we define a quantum family of homomorphisms of locally compact quantum groups. Roughly speaking, we show that such a family is classical. The purely algebraic counterpart of the discussed notion, i.e. a quantum family of homomorphisms of Hopf algebras, is introduced and the algebraic counterpart of the aforementioned result is proved. Moreover, we show that a quantum family of homomorphisms of Hopf algebras is consistent with the counits and coinverses of the given Hopf algebras. We compare our concept withweak coactionsintroduced by Andruskiewitsch and we apply it to the analysis of adjoint coaction. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
00927872
Volume :
45
Issue :
4
Database :
Complementary Index
Journal :
Communications in Algebra
Publication Type :
Academic Journal
Accession number :
119783750
Full Text :
https://doi.org/10.1080/00927872.2016.1222403