We give equivalent and sufficient criteria for the automorphism group of a complete toric variety, respectively a Gorenstein toric Fano variety, to be reductive. In particular we show that the automorphism group of a Gorenstein toric Fano variety is reductive, if the barycenter of the associated reflexive polytope is zero. Furthermore a sharp bound on the dimension of the reductive automorphism...

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 consider complex Kobayashi-hyperbolic manifolds of dimension n ≥ 2 for which the dimension of the group of holomorphic au-tomorphisms is equal to n 2 − 1. We give a complete classification of such manifolds for n ≥ 3 and discuss several examples for n = 2. 0 Introduction Let M be a connected complex manifold and Aut(M) the group of holomor-phic automorphisms of M. If M is Kobayashi-hyperboli...

Abstract We show that the automorphism group of a linking system associated to saturated fusion $\mathcal {F}$ depends only on as long object set is $\mathrm {Aut}(\mathcal {F})$ -invariant. This was known be true for systems in Oliver’s definition, but we demonstrate result holds also considerably more general definition introduced previously by author this article. A similar proved localities...

Throughout this paper L will be an algebraically closed field and K an algebraically closed subfield such that the transcendence rank of L over K is at least 3. In [4] we considered the pregeometry G(L/K) = (L,clK), where, for Y a subset of L, the closure clK( Y) is the algebraic closure in L of the subfield generated by K and Y. In this paper we shall be concerned mainly with the geometry G(L/...

We consider complex Kobayashi-hyperbolic manifolds of dimension n ≥ 2 for which the dimension of the group of holomorphic au-tomorphisms is equal to n 2 − 1. We give a complete classification of such manifolds for n ≥ 3 and discuss several examples for n = 2. 0 Introduction Let M be a connected complex manifold and Aut(M) the group of holomor-phic automorphisms of M. If M is Kobayashi-hyperboli...

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...