✦ LIBER ✦

Spherical Categories

✍ Scribed by John W Barrett; Bruce W Westbury

Publisher: Elsevier Science
Year: 1999
Tongue: English
Weight: 159 KB
Volume: 143
Category: Article
ISSN: 0001-8708
DOI: 10.1006/aima.1998.1800

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✦ Synopsis

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.

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