scholarly journals Towards a loop representation of connection theories defined over a super Lie algebra

1996 ◽  
Author(s):  
Luis F. Urrutia
Keyword(s):  
Lie Algebra ◽  
Super Lie Algebra

scholarly journals SUPER TENSOR MODELS, SUPER FUZZY SPACES AND SUPER n-ARY TRANSFORMATIONS

2011 ◽  
Vol 26 (24) ◽  
pp. 4203-4216 ◽  
Author(s):  
NAOKI SASAKURA
Keyword(s):  
Lie Algebra ◽  
General Framework ◽  
Space Form ◽  
Quantum Corrections ◽  
Physical Interest ◽  
Dynamical Generation ◽  
Fuzzy Space ◽  
Tensor Models ◽  
Algebraic Description ◽  
Super Lie Algebra

By extending the algebraic description of the bosonic rank-three tensor models, a general framework for super rank-three tensor models and correspondence to super fuzzy spaces is proposed. The corresponding super fuzzy spaces must satisfy a certain cyclicity condition on the algebras of functions on them. Due to the cyclicity condition, the symmetry of the super rank-three tensor models are represented by super n-ary transformations. The Leibnitz rules and the fundamental identities for the super n-ary transformations are discussed from the perspective of the symmetry of the algebra of a fuzzy space. It is shown that the super n-ary transformations of finite orders which conserve the algebra of a fuzzy space form a finite closed n-ary super Lie algebra. Super rank-three tensor models would be of physical interest as background independent models for dynamical generation of supersymmetric fuzzy spaces, in which quantum corrections are under control.

scholarly journals EXTENSIONS OF 2D GRAVITY

1994 ◽  
Vol 03 (01) ◽  
pp. 107-119
Author(s):  
Alexander Sevrin
Keyword(s):  
Large Class ◽  
Lie Algebra ◽  
Effective Action ◽  
2D Gravity ◽  
Exact Expression ◽  
Two Dimensions ◽  
Super Lie Algebra

After reviewing some aspects of gravity in two dimensions, I show that non-trivial embeddings of sl(2) in a semi-simple (super) Lie algebra give rise to a very large class of extensions of 2D gravity. The induced action is constructed as a gauged WZW model and an exact expression for the effective action is given.

(2+1)-dimensional supersymmetric integrable equations

2016 ◽  
Vol 14 (01) ◽  
pp. 1750013
Author(s):  
Zhao-Wen Yan ◽  
Tala ◽  
Fang Chen ◽  
Tao-Ran Liu ◽  
Jing-Min Han
Keyword(s):  
Lie Algebra ◽  
Bäcklund Transformations ◽  
Constraint Condition ◽  
Integrable Equations ◽  
Backlund Transformations ◽  
Homogenous Space ◽  
Super Lie Algebra

By means of two different approaches, we construct the (2+1)-dimensional supersymmetric integrable equations based on the super Lie algebra osp(3/2). We relax the constraint condition of homogenous space of super Lie algebra osp(3/2) in the first approach. In another one, the technique of extending the dimension of the systems is used. Furthermore for the [Formula: see text]-dimensional supersymmetric integrable equations, we also derive their Bäcklund transformations.

scholarly journals OCTONIONS AND SUPER-LIE ALGEBRA

1998 ◽  
Vol 13 (02) ◽  
pp. 223-231
Author(s):  
KHALED ABDEL-KHALEK
Keyword(s):  
Lie Algebra ◽  
Matrix Algebra ◽  
Yang Mills ◽  
Left And Right ◽  
Super Lie Algebra

We discuss how to represent the nonassociative octonionic structure in terms of the associative matrix algebra using the left and right octonionic operators. As an example we construct explicitly some Lie and super-Lie algebra. Then we discuss the notion of octonionic Grassmann numbers and explain its possible application for giving a superspace formulation of the minimal supersymmetric Yang–Mills models.

scholarly journals SOLUTIONS OF THE YANG-BAXTER EQUATIONS FROM BRAIDED-LIE ALGEBRAS AND BRAIDED GROUPS

1995 ◽  
Vol 04 (04) ◽  
pp. 673-697 ◽  
Author(s):  
SHAHN MAJID
Keyword(s):  
Hopf Algebra ◽  
Lie Algebra ◽  
Lie Algebras ◽  
Braid Group ◽  
Matrix Representation ◽  
R Matrix ◽  
Braided Hopf Algebra ◽  
Artin Braid Group ◽  
Braided Lie Algebras ◽  
Super Lie Algebra

We obtain an R-matrix or matrix representation of the Artin braid group acting in a canonical way on the vector space of every (super)-Lie algebra or braided-Lie algebra. The same result applies for every (super)-Hopf algebra or braided-Hopf algebra. We recover some known representations such as those associated to racks. We also obtain new representations such as a non-trivial one on the ring k[x] of polynomials in one variable, regarded as a braided-line. Representations of the extended Artin braid group for braids in the complement of S1 are also obtained by the same method.

Integrable two-dimensional dynamical systems and the characteristic Lie algebras

2007 ◽  
Vol 5 ◽  
pp. 195-200
Author(s):  
A.V. Zhiber ◽  
O.S. Kostrigina
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Lie Algebra ◽  
Lie Algebras ◽  
Second Order ◽  
System Of Equations ◽  
Two Dimensional ◽  
Finite Dimensional ◽  
Dimensional Dynamical System

In the paper it is shown that the two-dimensional dynamical system of equations is Darboux integrable if and only if its characteristic Lie algebra is finite-dimensional. The class of systems having a full set of fist and second order integrals is described.

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