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Quantum families of quantum group homomorphisms.
- 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]
- Subjects :
- QUANTUM groups
HOMOMORPHISMS
C*-algebras
HOPF algebras
GROUP theory
Subjects
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