UNSPECIFIED (1999) Spherical categories. ADVANCES IN MATHEMATICS, 143 (2). pp. 357-375. ISSN 0001-8708

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Abstract

This paper is a study of monoidal categories with duals where the tensor product need not be commutative. The motivating examples are categories of representations of Hopf algebras. We introduce the new notion of a spherical category. In the first section we prove a coherence theorem for a monoidal category with duals following S. MacLane (1963, Rice Univ. Stud. 49, 28-46). In the second section we give the definition of a spherical category, and construct a natural quotient which is also spherical. In the third section we define spherical Hopf algebras so that the category of representations is spherical. Examples of spherical Hopf algebras are involutory Hopf algebras and ribbon Hopf algebras. Finally we study the natural quotient in these cases and show it is semisimple. (C) 1999 Academic Press.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Journal or Publication Title:	ADVANCES IN MATHEMATICS
Publisher:	ACADEMIC PRESS INC
ISSN:	0001-8708
Date:	10 May 1999
Volume:	143
Number:	2
Number of Pages:	19
Page Range:	pp. 357-375
Publication Status:	Published
URI:	http://wrap.warwick.ac.uk/id/eprint/14563

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