Morita equivalence classes of $2$-blocks of defect three

Morita equivalence classes of 2-blocks of defect three

We give a complete description of the Morita equivalence classes of blocks with elementary abelian defect groups of order 8 and of the derived equivalences between them. A consequence is the verification of Broué’s abelian defect group conjecture for these blocks. It also completes the classification of Morita and derived equivalence classes of 2-blocks of defect at most three defined over a su...

The graph of equivalence classes and Isoclinism of groups

‎Let $G$ be a non-abelian group and let $Gamma(G)$ be the non-commuting graph of $G$‎. ‎In this paper we define an equivalence relation $sim$ on the set of $V(Gamma(G))=Gsetminus Z(G)$ by taking $xsim y$ if and only if $N(x)=N(y)$‎, ‎where $ N(x)={uin G | x textrm{ and } u textrm{ are adjacent in }Gamma(G)}$ is the open neighborhood of $x$ in $Gamma(G)$‎. ‎We introduce a new graph determined ...

ul 2 01 5 A SYNTACTIC CHARACTERIZATION OF MORITA EQUIVALENCE

We characterize Morita equivalence of theories in the sense of Johnstone in [24] in terms of a new syntactic notion of a common definitional extension developed by Barrett and Halvorson in [25] for cartesian, regular, coherent, geometric and first-order theories. This provides a purely syntactic characterization of the relation between two theories that have equivalent categories of models natu...

Some equivalence classes of operators on B(H)

Noncommutative fermions and Morita equivalence

We study the Morita equivalence for fermion theories on noncommutative two-tori. For rational values of the θ parameter (in appropriate units) we show the equivalence between an abelian noncommutative fermion theory and a nonabelian theory of twisted fermions on ordinary space. We study the chiral anomaly and compute the determinant of the Dirac operator in the dual theories showing that the Mo...