Equivariant extensions of *-algebras

Details Equivariant extensions of *-algebras Equivariant extensions of *-algebras

2010-03-30

arxiv.org/abs/1003.5778v2

New York J. Math. 16 (2010), p 369-385

Mathematics

K-Theory and Homology

12 pages

Scientific paper

A bivariant functor is defined on a category of *-algebras and a category of operator ideals, both with actions of a second countable group $G$, into the category of abelian monoids. The element of the bivariant functor will be $G$-equivariant extensions of a *-algebra by an operator ideal under a suitable equivalence relation. The functor is related with the ordinary $Ext$-functor for $C^*$-algebras defined by Brown-Douglas-Fillmore. Invertibility in this monoid is studied and characterized in terms of Toeplitz operators with abstract symbol.

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