scholarly journals Automorphisms of n-Ary Groups

2021 ◽  
Vol 77 (1) ◽  
Author(s):  
Wieslaw A. Dudek
Keyword(s):  
Group Of Automorphisms

AbstractIsotopies and autotopies of n-ary groups are described. As a consequence, we obtain various characterizations of the group of automorphisms of n-ary groups. We also determine the number of automorphisms of a given n-ary group.

scholarly journals Constructions for arc-transitive digraphs

1995 ◽  
Vol 59 (1) ◽  
pp. 61-80 ◽  
Author(s):  
Marston Conder ◽  
Peter Lorimer ◽  
Cheryl Praeger
Keyword(s):  
Positive Integer ◽  
Permutation Group ◽  
Finite Groups ◽  
Transitive Permutation Group ◽  
Group Of Automorphisms ◽  
Representations Of Finite Groups ◽  
Regular Digraph

AbstractA number of constructions are given for arc-transitive digraphs, based on modifications of permutation representations of finite groups. In particular, it is shown that for every positive integer s and for any transitive permutation group p of degree k, there are infinitely many examples of a finite k-regular digraph with a group of automorphisms acting transitively on s-arcs (but not on (s + 1)-arcs), such that the stabilizer of a vertex induces the action of P on the out-neighbour set.

The group of automorphisms of a commutative algebra

1995 ◽  
Vol 219 (1) ◽  
pp. 31-48 ◽  
Author(s):  
Francisco Guil-Asensio ◽  
Manuel Saorín
Keyword(s):  
Commutative Algebra ◽  
Group Of Automorphisms

scholarly journals A note on the fixed subring of an FPF ring

1989 ◽  
Vol 40 (1) ◽  
pp. 109-111 ◽  
Author(s):  
John Clark
Keyword(s):  
Finite Group ◽  
Associative Ring ◽  
Finitely Generated ◽  
Group Of Automorphisms ◽  
Direct Sum ◽  
Epimorphic Image ◽  
A Finite Group

An associative ring R with identity is called a left (right) FPF ring if given any finitely generated faithful left (right) R-module A and any left (right) R-module M then M is the epimorphic image of a direct sum of copies of A. Faith and Page have asked if the subring of elements fixed by a finite group of automorphisms of an FPF ring need also be FPF. Here we present examples showing the answer to be negative in general.

scholarly journals Deformation quantization of principal bundles

2016 ◽  
Vol 13 (08) ◽  
pp. 1630010
Author(s):  
Paolo Aschieri
Keyword(s):  
Quantum Group ◽  
Deformation Quantization ◽  
Principal Bundle ◽  
Base Space ◽  
Structure Group ◽  
Galois Extensions ◽  
Principal Bundles ◽  
Group Of Automorphisms ◽  
Drinfeld Twist

We outline how Drinfeld twist deformation techniques can be applied to the deformation quantization of principal bundles into noncommutative principal bundles and, more in general, to the deformation of Hopf–Galois extensions. First, we twist deform the structure group in a quantum group, and this leads to a deformation of the fibers of the principal bundle. Next, we twist deform a subgroup of the group of automorphisms of the principal bundle, and this leads to a noncommutative base space. Considering both deformations, we obtain noncommutative principal bundles with noncommutative fiber and base space as well.

scholarly journals The Group of Automorphisms of the Algebra of one-Sided Inverses of a Polynomial Algebra. II

2015 ◽  
Vol 58 (3) ◽  
pp. 543-580
Author(s):  
V. V. Bavula
Keyword(s):  
Weyl Algebra ◽  
Differential Operators ◽  
Polynomial Algebra ◽  
Group Of Automorphisms ◽  
Algebra Ii ◽  
Noetherian Property

AbstractThe algebra of one-sided inverses of a polynomial algebra Pn in n variables is obtained from Pn by adding commuting left (but not two-sided) inverses of the canonical generators of the algebra Pn. The algebra is isomorphic to the algebra of scalar integro-differential operators provided that char(K) = 0. Ignoring the non-Noetherian property, the algebra belongs to a family of algebras like the nth Weyl algebra An and the polynomial algebra P2n. Explicit generators are found for the group Gn of automorphisms of the algebra and for the group of units of (both groups are huge). An analogue of the Jacobian homomorphism AutK-alg (Pn) → K* is introduced for the group Gn (notice that the algebra is non-commutative and neither left nor right Noetherian). The polynomial Jacobian homomorphism is unique. Its analogue is also unique for n > 2 but for n = 1, 2 there are exactly two of them. The proof is based on the following theorem that is proved in the paper:

The Ample Cone for a K3 Surface

2011 ◽  
Vol 63 (3) ◽  
pp. 481-499 ◽  
Author(s):  
Arthur Baragar
Keyword(s):  
Hausdorff Dimension ◽  
Number Field ◽  
K3 Surface ◽  
Picard Number ◽  
Asymptotic Growth ◽  
Group Of Automorphisms ◽  
Line Parallel ◽  
Ample Cone

Abstract In this paper, we give several pictorial fractal representations of the ample or K¨ahler cone for surfaces in a certain class of K3 surfaces. The class includes surfaces described by smooth (2, 2, 2) forms in ℙ1 × ℙ1 × ℙ1 defined over a sufficiently large number field K that have a line parallel to one of the axes and have Picard number four. We relate the Hausdorff dimension of this fractal to the asymptotic growth of orbits of curves under the action of the surface's group of automorphisms. We experimentally estimate the Hausdorff dimension of the fractal to be 1.296 ± .010.

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