Kac algebras are one of the standard setups for Tannaka duality involving functional analysis. In a spirit of generalizing Pontrjagin duality to nonabelian locally compact groups they generalize locally compact groups and their Tannaka duals in a framework of von Neumann algebras with additional structure where a multiplicative unitary plays a central role. They are named after George Kac.

The standard monograph on Kac algebras is

- M. Enock, J. M. Schwartz,
*Kac algebras and duality of locally compact groups*, Springer-Verlag, 1992, , x+257 pp. gBooks, MR94e:46001

See also

- Takehiko Yamanouchi,
*An example of Kac algebra actions on Von Neumann algebra*, Proc. Amer. Math. Soc..**119**, No. 2 (1993) 503-511 jstor - M. Enock, L. Vaînerman,
*Deformation of a Kac algebra by an abelian subgroup*, Commun.Math. Phys.**178**(1996) 571–595 doi - Leonid Vaĭnerman,
*2-cocycles and twisting of Kac algebras*, Commun. Math. Phys.**191**(1998) 697-721 doi - Teodor Banica,
*Compact Kac algebras and commuting squares*, J. Funct. Anal.**176**(2000) 80-99 arXiv:math.QA/9909156

A related, but different setup of Hopf-von Neumann algebras is in

- L. I. Vaĭnerman, G. I. Kac,
*Nonunimodular ring groups and Hopf-von Neumann algebras*,doi Math. USSR Sbornik**23**:2 (1974) 185 - Shahn Majid,
*Hopf-von Neumann algebra bicrossproducts, Kac algebra bicrossproducts and*classical Yang-Baxter equations_, J. Funct. Anal. 95 (1991) 291-319

category: algebra, functional analysis

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