Infinitedimensional representations of 2groups
 Language
 English.
 Imprint
 Providence, R.I. : American Mathematical Society, c2012.
 Physical description
 v, 120 p. : ill ; 26 cm.
 Series
 Memoirs of the American Mathematical Society ; no. 1032.
Access
Available online

Stacks

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QA3 .A57 NO.1032

Unknown
QA3 .A57 NO.1032
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Contributors
 Contributor
 Baez, John C., 1961
Contents/Summary
 Bibliography
 Includes bibliographical references.
 Publisher's Summary
 A "$2$group" is a category equipped with a multiplication satisfying laws like those of a group. Just as groups have representations on vector spaces, $2$groups have representations on "$2$vector spaces", which are categories analogous to vector spaces. Unfortunately, Lie $2$groups typically have few representations on the finitedimensional $2$vector spaces introduced by Kapranov and Voevodsky. For this reason, Crane, Sheppeard and Yetter introduced certain infinitedimensional $2$vector spaces called "measurable categories" (since they are closely related to measurable fields of Hilbert spaces), and used these to study infinitedimensional representations of certain Lie $2$groups. Here they continue this work. They begin with a detailed study of measurable categories. Then they give a geometrical description of the measurable representations, intertwiners and $2$intertwiners for any skeletal measurable $2$group. They study tensor products and direct sums for representations, and various concepts of subrepresentation. They describe direct sums of intertwiners, and subintertwinersfeatures not seen in ordinary group representation theory and study irreducible and indecomposable representations and intertwiners. They also study "irretractable" representationsanother feature not seen in ordinary group representation theory. Finally, they argue that measurable categories equipped with some extra structure deserve to be considered "separable $2$Hilbert spaces", and compare this idea to a tentative definition of $2$Hilbert spaces as representation categories of commutative von Neumann algebras.
(source: Nielsen Book Data)
Subjects
Bibliographic information
 Publication date
 2012
 Responsibility
 John C. Baez ... [et al.].
 Series
 Memoirs of the American Mathematical Society, 00659266 ; no. 1032
 Note
 "September 2012, volume 219, number 1032 (end of volume)."
 ISBN
 9780821872840 (alk. paper)
 0821872842 (alk. paper)