Related papers: Deformed Algebras from Inverse Schwinger Method
We present a method to construct explicitly L-infinity algebras governing simultaneous deformations of various kinds of algebraic structures and of their morphisms. It is an alternative to the heavy use of the operad machinery of the…
We discuss q-counterparts of the Gauss integrals, a new type of Gauss-Selberg sums at roots of unity, and q-deformations of Riemann's zeta. The paper contains general results, one-dimensional formulas, and remarks about the current projects…
We investigate formal deformations of certain classes of nonassociative algebras including classes of K[{\Sigma}3]-associative algebras, Lie-admissible algebras and anti-associative algebras. In a process which is similar to Poisson algebra…
For all three--dimensional Lie algebras the construction of generators in terms of functions on 4-dimensional real phase space is given with a realization of the Lie product in terms of Poisson brackets. This is the classical…
In this paper we give an alternative construction of a certain class of Deformed Double Current Algebras. These algebras are deformations of $U({\rm End}(\Bbbk^r)[x,y])$ and they were initially defined and studied by N.Guay in his papers.…
The intelligent states associated with the suq (1,1) and suq (2) q-deformed Lie algebra are investigated. The eigenvalue problem is also discussed.
The main purpose of this article is to develop an explicit derived deformation theory of algebraic structures at a high level of generality, encompassing in a common framework various kinds of algebras (associative, commutative, Poisson...)…
We present a deformed algebra related to the q-exponential and the q-logarithm functions that emerge from nonextensive statistical mechanics. We also develop a q-derivative (and consistently a q-integral) for which the q-exponential is an…
Some one- and two-parametric deformations of U[sl(2)] and their representations are considered. Interestingly, a newly introduced two-parametric deformation admits a class of infinite - dimensional representations which have no classical…
We propose the method for obtaining invariants of arbitrary representations of Lie groups that reduces this problem to known problems of linear algebra. The basis of this method is the idea of a special extension of the representation…
We investigate spin as algebraic structure within the q-deformed Poincare algebra, proceeding in the same manner as in the undeformed case. The q-Pauli-Lubanski vector, the q-spin Casimir, and the q-little algebras for the massless and the…
We develop the deformation theory of A_\infty algebras together with \infty inner products and identify a differential graded Lie algebra that controls the theory. This generalizes the deformation theories of associative algebras, A_\infty…
We develop the theory of versal deformations of dialgebras and describe a method for constructing a miniversal deformation of a dialgebra.
With a q-deformed quantum mechanical framework, features of the uncertainty relation and a novel formulation of the Schr\"odinger equation are considered.
Based on the quantum superspace construction of $q$-deformed algebra, we discuss a supersymmetric extension of the deformed Virasoro algebra, which is a subset of the $q$-$W_{\infty}$ algebra recently appeared in the context of…
Starting from gravity as a Chern-Simons action for the AdS algebra in five dimensions, it is possible to deform the theory through an expansion of the Lie algebra that leads to a system consisting of the Einstein-Hilbert action plus…
We present a deformation theory approach to the classification of kinematical Lie algebras in 3+1 dimensions and present calculations leading to the classifications of all deformations of the static kinematical Lie algebra and of its…
We define a new $q$-deformation of Brauer's centralizer algebra which contains Hecke algebras of type $A$ as unital subalgebras. We determine its generic structure as well as the structure of certain semisimple quotients. This is expected…
Starting from the classical r-matrix of the non-standard (or Jordanian) quantum deformation of the sl(2,R) algebra, new triangular quantum deformations for the real Lie algebras so(2,2), so(3,1) and iso(2,1) are simultaneously constructed…
We study formal deformations of hom-Lie-Rinehart algebras. The associated deformation cohomology that controls deformations is constructed using multiderivations of hom-Lie-Rinehart algebras.