Diagonal type conditions on group C$^*$-algebras

Diagonal Bases in Orlik-solomon Type Algebras

To encode an important property of the “no broken circuit bases” of the Orlik-Solomon-Terao algebras, András Szenes has introduced a particular type of bases, the so called “diagonal basis”. We prove that this definition extends naturally to a large class of algebras, the so called χ-algebras. Our definitions make also use of an “iterative residue formula” based on the matroidal operation of co...

On Type I C-algebras

the structure of lie derivations on c*-algebras

نشان می دهیم که هر اشتقاق لی روی یک c^*-جبر به شکل استاندارد است، یعنی می تواند به طور یکتا به مجموع یک اشتقاق لی و یک اثر مرکز مقدار تجزیه شود. کلمات کلیدی: اشتقاق، اشتقاق لی، c^*-جبر.

Gröbner and Diagonal Bases in Orlik-solomon Type Algebras

The Orlik-Solomon algebra of a matroid M is the quotient of the exterior algebra on the points by the ideal I(M) generated by the boundaries of the circuits of the matroid. There is an isomorphism between the OrlikSolomon algebra of a complex matroid and the cohomology of the complement of a complex arrangement of hyperplanes. In this article a generalization of the Orlik-Solomon algebras, call...

On Morita Equivalence of Group Actions on Locally C-algebras

In this paper, we prove that two continuous inverse limit actions α and β of a locally compact group G on the locally C-algebras A and B are strongly Morita equivalent if and only if there is a locally C-algebra C such that A and B appear as two complementary full corners of C and there is a continuous action γ of G on C which leaves A and B invariant such that γ|A = α and γ|B = β. This general...