ON SHAVRUKOV’S NON-ISOMORPHISM THEOREM FOR DIAGONALIZABLE ALGEBRAS

A Representation Theorem for Co-diagonalizable Algebras

This abstract is a summary of a lecture given at the Seminar of the Department of Logic and Methodology of Sciences, Wroc law University, 23 May 1985. The present work refers directly to the investigations of Buszkowski and Prucnal [1] and that of Esakia [2], generalizing their results. Our main representation theorem for co-diagonalizable algebras (Theorem 2) is obtained by application of cert...

On Isomorphism of Simplicial Complexes and Their Related Algebras

An isomorphism theorem for digraphs

A seminal result by Lovász states that two digraphs A and B (possibly with loops) are isomorphic if and only if for every digraph X the number of homomorphisms X → A equals the number of homomorphisms X → B. Lovász used this result to deduce certain cancellation properties for the direct product of digraphs. We develop an analogous result for the class of digraphs without loops, and with weak h...

A Classification of Tracially Approximate Splitting Interval Algebras. III. Uniqueness Theorem and Isomorphism Theorem

Motivated by Huaxin Lin’s axiomatization of AH-algebras, the class of TASI-algebras is introduced as the class of unital C*-algebras which can be tracially approximated by splitting interval algebras—certain sub-C*-algebras of interval algebras. It is shown that the class of simple separable nuclear TASI-algebras satisfying the UCT is classified by the Elliott invariant. As a consequence, any s...

Diagonalizable Derivations of Finite-dimensional Algebras Ii

When an algebra is graded by a group, any additive character of the group induces a diagonalizable derivation of the ring. This construction is studied in detail for the case of a path algebra modulo relations and its fundamental group. We describe an injection of the character group into the first cohomology group following Assem-de la Peña. Rather general conditions are determined, in this co...