On the Cohomology for the Witt Algebra W(1,1)

1994 ◽  
pp. 291-295 ◽  
Author(s):  
Daniel K. Nakano
Keyword(s):  
Witt Algebra

scholarly journals W-representation of Rainbow tensor model

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Bei Kang ◽  
Lu-Yao Wang ◽  
Ke Wu ◽  
Jie Yang ◽  
Wei-Zhong Zhao
Keyword(s):  
Partition Function ◽  
Matrix Model ◽  
Crucial Role ◽  
Elementary Function ◽  
Tensor Model ◽  
Witt Algebra ◽  
Virasoro Constraints ◽  
Compact Expression ◽  
Non Gaussian ◽  
Dual Expression

Abstract We analyze the rainbow tensor model and present the Virasoro constraints, where the constraint operators obey the Witt algebra and null 3-algebra. We generalize the method of W-representation in matrix model to the rainbow tensor model, where the operators preserving and increasing the grading play a crucial role. It is shown that the rainbow tensor model can be realized by acting on elementary function with exponent of the operator increasing the grading. We derive the compact expression of correlators and apply it to several models, i.e., the red tensor model, Aristotelian tensor model and r = 4 rainbow tensor model. Furthermore, we discuss the case of the non-Gaussian red tensor model and present a dual expression for partition function through differentiation.

scholarly journals CLASSIFICATION OF GRADED LEFT-SYMMETRIC ALGEBRAIC STRUCTURES ON WITT AND VIRASORO ALGEBRAS

2011 ◽  
Vol 22 (02) ◽  
pp. 201-222 ◽  
Author(s):  
XIAOLI KONG ◽  
HONGJIA CHEN ◽  
CHENGMING BAI
Keyword(s):  
Virasoro Algebra ◽  
Indecomposable Module ◽  
Multiplication Operators ◽  
Algebraic Structures ◽  
Witt Algebra ◽  
Left Multiplication ◽  
Symmetric Algebras ◽  
Nonlinear Math ◽  
Math Phys

We find that a compatible graded left-symmetric algebraic structure on the Witt algebra induces an indecomposable module V of the Witt algebra with one-dimensional weight spaces by its left-multiplication operators. From the classification of such modules of the Witt algebra, the compatible graded left-symmetric algebraic structures on the Witt algebra are classified. All of them are simple and they include the examples given by [Comm. Algebra32 (2004) 243–251; J. Nonlinear Math. Phys.6 (1999) 222–245]. Furthermore, we classify the central extensions of these graded left-symmetric algebras which give the compatible graded left-symmetric algebraic structures on the Virasoro algebra. They coincide with the examples given by [J. Nonlinear Math. Phys.6 (1999) 222–245].

Correlators in the β-deformed Gaussian Hermitian and complex matrix models

2019 ◽  
Vol 34 (33) ◽  
pp. 1950221 ◽  
Author(s):  
Ying Chen ◽  
Bei Kang ◽  
Min-Li Li ◽  
Li-Fang Wang ◽  
Chun-Hong Zhang
Keyword(s):  
Matrix Models ◽  
Integral Representations ◽  
Witt Algebra ◽  
Complex Matrix ◽  
Virasoro Constraints

We investigate the [Formula: see text]-deformed Gaussian Hermitian and [Formula: see text] complex matrix models which are defined as the eigenvalue integral representations. Their [Formula: see text] constraints are constructed such that the constraint operators yield the same [Formula: see text][Formula: see text]-algebra. When particularized to the Virasoro constraints in the [Formula: see text] constraints, the corresponding constraint operators yield the Witt algebra and null 3-algebra. By solving our Virasoro constraints, we derive the formulas for correlators in these two [Formula: see text]-deformed matrix models, respectively.

scholarly journals Ideals in the Enveloping Algebra of the Positive Witt Algebra

2019 ◽  
Vol 23 (4) ◽  
pp. 1569-1599
Author(s):  
Alexey V. Petukhov ◽  
Susan J. Sierra
Keyword(s):  
Witt Algebra ◽  
Enveloping Algebra

Derivations and Automorphism Group of Original Deformative Schrödinger-Virasoro Algebra

2015 ◽  
Vol 22 (03) ◽  
pp. 517-540 ◽  
Author(s):  
Qifen Jiang ◽  
Song Wang
Keyword(s):  
Automorphism Group ◽  
Lie Algebra ◽  
Direct Product ◽  
Virasoro Algebra ◽  
Witt Algebra ◽  
Tensor Density ◽  
Derivation Algebra

In this paper, we determine the derivation algebra and the automorphism group of the original deformative Schrödinger-Virasoro algebra, which is the semi-direct product Lie algebra of the Witt algebra and its tensor density module Ig(a,b).

scholarly journals The nilpotent commuting variety of the Witt algebra

2014 ◽  
Vol 218 (10) ◽  
pp. 1783-1791 ◽  
Author(s):  
Yu-Feng Yao ◽  
Hao Chang
Keyword(s):  
Witt Algebra ◽  
Commuting Variety

scholarly journals Ext1-quivers for the Witt algebra W(1,1)

2009 ◽  
Vol 322 (5) ◽  
pp. 1548-1564 ◽  
Author(s):  
Brian D. Boe ◽  
Daniel K. Nakano ◽  
Emilie Wiesner
Keyword(s):  
Witt Algebra

scholarly journals Identities of the left-symmetric Witt algebras

2016 ◽  
Vol 26 (02) ◽  
pp. 435-450 ◽  
Author(s):  
Daniyar Kozybaev ◽  
Ualbai Umirbaev
Keyword(s):  
Lie Algebras ◽  
Characteristic Zero ◽  
Polynomial Algebra ◽  
Witt Algebra ◽  
Symmetric Algebras ◽  
Algebra Over A Field

Let [Formula: see text] be the polynomial algebra over a field [Formula: see text] of characteristic zero in the variables [Formula: see text] and [Formula: see text] be the left-symmetric Witt algebra of all derivations of [Formula: see text] [D. Burde, Left-symmetric algebras, or pre-Lie algebras in geometry and physics, Cent. Eur. J. Math. 4(3) (2006) 323–357]. We describe all right operator identities of [Formula: see text] and prove that the set of all algebras [Formula: see text], where [Formula: see text], generates the variety of all left-symmetric algebras. We also describe a class of general (not only right operator) identities for [Formula: see text].

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