Results 31 to 40 of about 2,742,459 (94)

Four-Dimensional Spin Foam Perturbation Theory

Symmetry, Integrability and Geometry: Methods and Applications, 2011
We define a four-dimensional spin-foam perturbation theory for the BF-theory with a B∧B potential term defined for a compact semi-simple Lie group G on a compact orientable 4-manifold M.
João Faria Martins, Aleksandar Mikovic
doaj   +1 more source

Solving Particle–Antiparticle and Cosmological Constant Problems

Axioms
We solve the particle-antiparticle and cosmological constant problems proceeding from quantum theory, which postulates that: various states of the system under consideration are elements of a Hilbert space H with a positive definite metric; each physical
Felix M. Lev
doaj   +1 more source

Euler's difference table and decomposition of tensor powers of adjoint representation of $A_n$ Lie algebra [PDF]

arXiv, 2019
By using of Euler's difference table, we obtain simple explicit formula for the decomposition of $k$-th tensor power of adjoint representation of $A_n$ Lie algebra at $2 k \le{n+1}$.
arxiv  

Lax Integrable Supersymmetric Hierarchies on Extended Phase Spaces

Symmetry, Integrability and Geometry: Methods and Applications, 2006
We obtain via Bäcklund transformation the Hamiltonian representation for a Lax type nonlinear dynamical system hierarchy on a dual space to the Lie algebra of super-integral-differential operators of one anticommuting variable, extended by evolutions of ...
Oksana Ye. Hentosh
doaj  

Representations of Bihom-Lie algebras [PDF]

arXiv, 2016
Bihom-Lie algebra is a generalized Hom-Lie algebra endowed with two commuting multiplicative linear maps. In this paper, we study cohomology and representations of Bihom-Lie algebras. In particular, derivations, central extensions, derivation extensions, the trivial representation and the adjoint representation of Bihom-Lie algebras are studied in ...
arxiv  

Hom-Lie Algebras with Symmetric Invariant NonDegenerate Bilinear Forms [PDF]

arXiv, 2010
The aim of this paper is to introduce and study quadratic Hom-Lie algebras, which are Hom-Lie algebras with symmetric invariant nondegenerate bilinear forms. We provide several constructions leading to examples and extend the double extension theory to Hom-Lie algebras.
arxiv  

Inonu-Wigner Contractions of Kac-Moody Algebras

, 1992
We discuss In\"on\"u-Wigner contractions of affine Kac-Moody algebras. We show that the Sugawara construction for the contracted affine algebra exists only for a fixed value of the level $k$, which is determined in terms of the dimension of the ...
Majumdar, Parthasarathi
core   +1 more source

Euler's triangle and the decomposition of tensor powers of adjoint representation of $A_1$ Lie algebra [PDF]

arXiv, 2019
We consider the relation between Euler's trinomial problem and the problem of decomposition of tensor powers of adjoint representation of $A_1$ Lie algebra. By using this approach, some new results for both problems are obtained.
arxiv  

Constructing Graded Lie Algebras [PDF]

arXiv, 2004
The Z-grading determined by a long simple root of an affine or finite type Lie algebra arises from an adjoint or cominuscule representation of a lower rank semi-simple complex Lie algebra. Analysis of the relationship between the grading and the representation leads to an extension of Kac's construction of nontwisted affine Lie algebras.
arxiv  

From $\mathcal{O}$-operators of 3-Dimensional 3-Lie algebras to 3-Pre-Lie algebras

, 2023
In this paper, we explicitly determine all $\mathcal{O}$-operators with respect to the adjoint representation of 3-dimensional complex 3-Lie algebras. Furthermore, we provide the induced 3-Pre-Lie algebra structures and the corresponding solutions of the
Chuangchuang, Kang, Jiafeng, Lü, Ziying, Cheng   +2 more
core