منابع مشابه
Skew Products and Crossed Products by Coactions
Given a labeling c of the edges of a directed graph E by elements of a discrete group G, one can form a skew-product graph E ×c G. We show, using the universal properties of the various constructions involved, that there is a coaction δ of G on C∗(E) such that C∗(E ×c G) is isomorphic to the crossed product C ∗(E) ×δ G. This isomorphism is equivariant for the dual action δ̂ and a natural action ...
متن کاملCrossed complexes, free crossed resolutions and graph products of groups
The category of crossed complexes gives an algebraic model of CW -complexes and cellular maps. Free crossed resolutions of groups contain information on a presentation of the group as well as higher homological information. We relate this to the problem of calculating non-abelian extensions. We show how the strong properties of this category allow for the computation of free crossed resolutions...
متن کاملTraces of Matrix Products
Given two noncommuting matrices, A and B, it is well known that AB and BA have the same trace. This extends to cyclic permutations of products of A’s and B’s. It is shown here that for 2 × 2 matrices A and B, whose elements are independent random variables with standard normal distributions, the probability that Tr(ABAB) > Tr(AB) is exactly 1 √ 2 .
متن کاملCrossed Products by a Coalgebra
We introduce the notion of a crossed product of an algebra by a coalgebra C, which generalises the notion of a crossed product by a bialgebra well-studied in the theory of Hopf algebras. The result of such a crossed product is an algebra which is also a right C-comodule. We find the necessary and sufficient conditions for two coalgebra crossed products be equivalent. We show that the two-dimens...
متن کاملFull Crossed Products by Coactions,
Let δ be a coaction of a locally compact group G on a C*-algebra A. We show that if I is a δ-invariant ideal in A, then 0! I¬δ I G!A¬δ G! (A}I )¬δI G! 0 for full crossed products, as Landstad et al. have done for spatial crossed products by coactions. We prove that for suitable coactions, the crossed products of C ! (X )-algebras are again C ! (X )-algebras, and the crossed products of continuo...
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ژورنال
عنوان ژورنال: Indiana University Mathematics Journal
سال: 2019
ISSN: 0022-2518
DOI: 10.1512/iumj.2019.68.7759