A skew Calabi-Yau algebra is a generalization of a Calabi-Yau algebra which allows for a non-trivial Nakayama automorphism. We prove three homological identities about the Nakayama automorphism and give several applications. The identities we prove show (i) how the Nakayama automorphism of a smash product algebra A#H is related to the Nakayama automorphisms of a graded skew Calabi-Yau algebra A...

Let D be a symmetric 2-(121, 16, 2) design with the automorphism group of Aut(D). In this paper the order of automorphism of prime order of Aut(D) is studied, and some results are obtained about the number of fixed points of these automorphisms. Also we will show that |Aut(D)|=2p 3q 5r 7s 11t 13u, where p, q, r, s, t and u are non-negative integers such that r, s, t, u ? 1. In addition we prese...

We relate the character theory of symmetric groups S2n and S2n+1 with that hyperoctahedral group Bn=(Z/2)n⋊Sn, as part expectation reductive diagram automorphism their Weyl groups, is related to fixed subgroup automorphism.

In the first paper in this series a structure S was called canonically reconstructible from a structure T provided 5 was canonically isomorphic to a structure T' derived from T. The principle proposition of the paper was the scholium which asserted: If a structure 5 contains a substructure T and if S is canonically reconstructible from T, then every automorphism of T may be extended uniquely to...

In this paper, we will determine the full automorphism groups of rose window graphs that are not edge-transitive. As the full automorphism groups of edge-transitive rose window graphs have been determined, this will complete the problem of calculating the full automorphism group of rose window graphs. As a corollary, we determine which rose window graphs are vertex-transitive. Finally, we deter...

There are 50,024 Kirkman triple systems of order 21 admitting an automorphism of order 2. There are 13,280 Kirkman triple systems of order 21 admitting an automorphism of order 3. Together with the 192 known systems and some simple exchange operations, this leads to a collection of 63,745 nonisomorphic Kirkman triple systems of order 21. This includes all KTS(21)s having a nontrivial automorphi...

For partial automorphisms of C∗-algebras, Takai-Takesaki crossed product duality tends to fail, in proportion to the extent to which the partial automorphism is not an automorphism.

The problem of finding minimal vertex number of graphs with a given automorphism group is addressed in this article for the case of cyclic groups. This problem was considered earlier by other authors. We give a construction of an undirected graph having 4n+ 6 vertices and automorphism group cyclic of order 4n, n ≥ 1. As a special case we get graphs with 2k + 6 vertices and cyclic automorphism g...

Let X and Y be infinite graphs, such that the automorphism group of X is nonamenable, and the automorphism group of Y has an infinite orbit. We prove that there is no automorphism-invariant measure on the set of spanning trees in the direct product X × Y . This implies that the minimal spanning forest corresponding to i.i.d. edge-weights in such a product, has infinitely many connected componen...