scholarly journals On the Automorphism Group of the First Weyl Algebra

2013 ◽  
Vol 42 (1) ◽  
pp. 81-95 ◽  
Author(s):  
M. K. Kouakou ◽  
A. Tchoudjem
Keyword(s):  
Automorphism Group ◽  
Weyl Algebra

scholarly journals Automorphisms for Some Symmetric Multiparameter Quantized Weyl Algebras and Their Localizations

2017 ◽  
Vol 24 (03) ◽  
pp. 419-438 ◽  
Author(s):  
Xin Tang
Keyword(s):  
Automorphism Group ◽  
Weyl Algebra ◽  
Isomorphism Problem ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Polynomial Extension ◽  
Localization Formula ◽  
Weyl Algebras ◽  
Necessary And Sufficient ◽  
Quantized Weyl Algebra

We study a family of “symmetric” multiparameter quantized Weyl algebras [Formula: see text] and some related algebras. We compute the Nakayama automorphism of [Formula: see text], give a necessary and sufficient condition for [Formula: see text] to be Calabi-Yau, and prove that [Formula: see text] is cancellative. We study the automorphisms and isomorphism problem for [Formula: see text] and [Formula: see text]. Similar results are established for the Maltsiniotis multiparameter quantized Weyl algebra [Formula: see text] and its polynomial extension. We prove a quantum analogue of the Dixmier conjecture for a simple localization [Formula: see text] and determine its automorphism group.

scholarly journals Actions of the additive group Ga on certain noncommutative deformations of the plane

2021 ◽  
Vol 29 (2) ◽  
pp. 269-279
Author(s):  
Ivan Kaygorodov ◽  
Samuel A. Lopes ◽  
Farukh Mashurov
Keyword(s):  
Automorphism Group ◽  
Polynomial Ring ◽  
Characteristic Zero ◽  
Weyl Algebra ◽  
Additive Group ◽  
Prime Characteristic ◽  
Arbitrary Characteristic ◽  
Arbitrary Polynomial ◽  
Comodule Algebra ◽  
The Family

Abstract We connect the theorems of Rentschler [18] and Dixmier [10] on locally nilpotent derivations and automorphisms of the polynomial ring A 0 and of the Weyl algebra A 1, both over a field of characteristic zero, by establishing the same type of results for the family of algebras A h = 〈 x , y | y x − x y = h ( x ) 〉 , {A_h} = \left\langle {x,y|yx - xy = h\left( x \right)} \right\rangle , , where h is an arbitrary polynomial in x. In the second part of the paper we consider a field 𝔽 of prime characteristic and study 𝔽[t]-comodule algebra structures on Ah . We also compute the Makar-Limanov invariant of absolute constants of Ah over a field of arbitrary characteristic and show how this subalgebra determines the automorphism group of Ah .

scholarly journals PRIMITIVE IDEALS AND AUTOMORPHISM GROUP OF $U_{q}^{+}(B_{2})$

2007 ◽  
Vol 06 (01) ◽  
pp. 21-47 ◽  
Author(s):  
STÉPHANE LAUNOIS
Keyword(s):  
Automorphism Group ◽  
Weyl Algebra ◽  
Classical Case ◽  
Ground Field ◽  
Positive Part ◽  
Enveloping Algebra ◽  
Simple Factor ◽  
Dimension 2 ◽  
Invertible Elements ◽  
Kirillov Dimension

Let 𝔤 be a complex simple Lie algebra of type B2 and q be a nonzero complex number which is not a root of unity. In the classical case, a theorem of Dixmier asserts that the simple factor algebras of Gelfand–Kirillov dimension 2 of the positive part U+(𝔤) of the enveloping algebra of 𝔤 are isomorphic to the first Weyl algebra. In order to obtain some new quantized analogues of the first Weyl algebra, we explicitly describe the prime and primitive spectra of the positive part [Formula: see text] of the quantized enveloping algebra of 𝔤 and then we study the simple factor algebras of Gelfand–Kirillov dimension 2 of [Formula: see text]. In particular, we show that the centers of such simple factor algebras are reduced to the ground field ℂ and we compute their group of invertible elements. These computations allow us to prove that the automorphism group of [Formula: see text] is isomorphic to the torus (ℂ*)2, as conjectured by Andruskiewitsch and Dumas.

scholarly journals On the automorphism group of a symplectic half-flat 6-manifold

2019 ◽  
Vol 31 (1) ◽  
pp. 265-273
Author(s):  
Fabio Podestà ◽  
Alberto Raffero
Keyword(s):  
Automorphism Group ◽  
Lie Algebra ◽  
Group Action ◽  
Cohomogeneity One ◽  
Cohomogeneity One Action

Abstract We prove that the automorphism group of a compact 6-manifold M endowed with a symplectic half-flat {\mathrm{SU}(3)} -structure has Abelian Lie algebra with dimension bounded by {\min\{5,b_{1}(M)\}} . Moreover, we study the properties of the automorphism group action and we discuss relevant examples. In particular, we provide new complete examples on {T\mathbb{S}^{3}} which are invariant under a cohomogeneity one action of {\mathrm{SO}(4)} .

scholarly journals ON EDGE-PRIMITIVE GRAPHS WITH SOLUBLE EDGE-STABILIZERS

2021 ◽  
pp. 1-28
Author(s):  
HUA HAN ◽  
HONG CI LIAO ◽  
ZAI PING LU
Keyword(s):  
Automorphism Group

Abstract A graph is edge-primitive if its automorphism group acts primitively on the edge set, and $2$ -arc-transitive if its automorphism group acts transitively on the set of $2$ -arcs. In this paper, we present a classification for those edge-primitive graphs that are $2$ -arc-transitive and have soluble edge-stabilizers.

scholarly journals Affine cones over cubic surfaces are flexible in codimension one

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Alexander Perepechko
Keyword(s):  
Automorphism Group ◽  
Open Subset ◽  
Pezzo Surface ◽  
Ample Divisor ◽  
Transitive Action ◽  
Del Pezzo Surface ◽  
Codimension One ◽  
Cubic Surfaces ◽  
Special Automorphism ◽  
Del Pezzo

AbstractLet Y be a smooth del Pezzo surface of degree 3 polarized by a very ample divisor that is not proportional to the anticanonical one. Then the affine cone over Y is flexible in codimension one. Equivalently, such a cone has an open subset with an infinitely transitive action of the special automorphism group on it.

Automorphism group and representation of a twisted multi-loop algebra

2010 ◽  
Vol 26 (1) ◽  
pp. 143-154 ◽  
Author(s):  
Cui Chen ◽  
Hai Feng Lian ◽  
Shao Bin Tan
Keyword(s):  
Automorphism Group ◽  
Loop Algebra
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