Generically Laurent polynomial algebras over a D.V.R. which are not quasi Laurent polynomial algebras

2014 ◽  
Vol 218 (4) ◽  
pp. 651-660
Author(s):  
Asawari M. Abhyankar ◽  
S.M. Bhatwadekar
Keyword(s):  
Laurent Polynomial ◽  
Polynomial Algebras

scholarly journals A note on quasi Laurent polynomial algebras in n variables

2014 ◽  
Vol 6 (2) ◽  
pp. 127-147
Author(s):  
A.M. Abhyankar ◽  
S.M. Bhatwadekar
Keyword(s):  
Laurent Polynomial ◽  
Polynomial Algebras

scholarly journals Biderivations of the higher rank Witt algebra without anti-symmetric condition

2018 ◽  
Vol 16 (1) ◽  
pp. 447-452 ◽  
Author(s):  
Xiaomin Tang ◽  
Yu Yang
Keyword(s):  
Lie Algebra ◽  
Laurent Polynomial ◽  
Low Rank ◽  
Witt Algebra ◽  
Polynomial Algebras ◽  
Derivation Algebra ◽  
Higher Rank

AbstractThe Witt algebra 𝔚d of rank d(≥ 1) is the derivation algebra of Laurent polynomial algebras in d commuting variables. In this paper, all biderivations of 𝔚d without anti-symmetric condition are determined. As an applications, commutative post-Lie algebra structures on 𝔚d are obtained. Our conclusions recover and generalize results in the related papers on low rank or anti-symmetric cases.

scholarly journals LAURENT POLYNOMIAL LANDAU–GINZBURG MODELS FOR COMINUSCULE HOMOGENEOUS SPACES

2021 ◽  
Author(s):  
PETER SPACEK
Keyword(s):  
Homogeneous Space ◽  
Homogeneous Spaces ◽  
Laurent Polynomial ◽  
Complete Intersections ◽  
Laurent Polynomials ◽  
Young Diagrams ◽  
Similar Shape ◽  
Algebraic Torus ◽  
The One ◽  
Polynomial Potentials

AbstractIn this article we construct Laurent polynomial Landau–Ginzburg models for cominuscule homogeneous spaces. These Laurent polynomial potentials are defined on a particular algebraic torus inside the Lie-theoretic mirror model constructed for arbitrary homogeneous spaces in [Rie08]. The Laurent polynomial takes a similar shape to the one given in [Giv96] for projective complete intersections, i.e., it is the sum of the toric coordinates plus a quantum term. We also give a general enumeration method for the summands in the quantum term of the potential in terms of the quiver introduced in [CMP08], associated to the Langlands dual homogeneous space. This enumeration method generalizes the use of Young diagrams for Grassmannians and Lagrangian Grassmannians and can be defined type-independently. The obtained Laurent polynomials coincide with the results obtained so far in [PRW16] and [PR13] for quadrics and Lagrangian Grassmannians. We also obtain new Laurent polynomial Landau–Ginzburg models for orthogonal Grassmannians, the Cayley plane and the Freudenthal variety.

scholarly journals Gelfand-Kirillov Dimensions of Modules over Differential Difference Algebras

2016 ◽  
Vol 23 (04) ◽  
pp. 701-720 ◽  
Author(s):  
Xiangui Zhao ◽  
Yang Zhang
Keyword(s):  
Computational Method ◽  
Finitely Generated ◽  
Finitely Generated Module ◽  
Polynomial Algebras ◽  
Ore Extensions ◽  
Basis Method ◽  
Finitely Generated Modules ◽  
Kirillov Dimension

Differential difference algebras are generalizations of polynomial algebras, quantum planes, and Ore extensions of automorphism type and of derivation type. In this paper, we investigate the Gelfand-Kirillov dimension of a finitely generated module over a differential difference algebra through a computational method: Gröbner-Shirshov basis method. We develop the Gröbner-Shirshov basis theory of differential difference algebras, and of finitely generated modules over differential difference algebras, respectively. Then, via Gröbner-Shirshov bases, we give algorithms for computing the Gelfand-Kirillov dimensions of cyclic modules and finitely generated modules over differential difference algebras.

scholarly journals FRIEZES, STRINGS AND CLUSTER VARIABLES

2011 ◽  
Vol 54 (1) ◽  
pp. 27-60 ◽  
Author(s):  
IBRAHIM ASSEM ◽  
GRÉGOIRE DUPONT ◽  
RALF SCHIFFLER ◽  
DAVID SMITH
Keyword(s):  
Laurent Polynomial ◽  
Tilted Algebra ◽  
String Module ◽  
Cluster Character

AbstractTo any walk in a quiver, we associate a Laurent polynomial. When the walk is the string of a string module over a 2-Calabi–Yau tilted algebra, we prove that this Laurent polynomial coincides with the corresponding cluster character of the string module up to an explicit normalising monomial factor.

Spherical functions and local densities on the space of p-adic quaternion Hermitian forms

2021 ◽  
pp. 1-38
Author(s):  
Yumiko Hironaka
Keyword(s):  
Laurent Polynomial ◽  
Spherical Functions ◽  
Plancherel Formula ◽  
Explicit Formulas ◽  
Hermitian Forms ◽  
Spherical Fourier Transform ◽  
Local Densities ◽  
Laurent Polynomial Ring ◽  
Injective Map ◽  
Residual Characteristic

We introduce the space [Formula: see text] of quaternion Hermitian forms of size [Formula: see text] on a [Formula: see text]-adic field with odd residual characteristic, and define typical spherical functions [Formula: see text] on [Formula: see text] and give their induction formula on sizes by using local densities of quaternion Hermitian forms. Then, we give functional equation of spherical functions with respect to [Formula: see text], and define a spherical Fourier transform on the Schwartz space [Formula: see text] which is Hecke algebra [Formula: see text]-injective map into the symmetric Laurent polynomial ring of size [Formula: see text]. Then, we determine the explicit formulas of [Formula: see text] by a method of the author’s former result. In the last section, we give precise generators of [Formula: see text] and determine all the spherical functions for [Formula: see text], and give the Plancherel formula for [Formula: see text].

Sign in / Sign up

Export Citation Format

Share Document