Derivation problem for quandle algebras

Journal of Algebra, 2000

some applications of the main results to the study of functions f ∈ Hom L L such that f • µ or µ • f ∧ I L defines a Lie multiplication.

1998

This paper is a continuation of "Quantization of Lie bialgebras I-IV". The goal of this paper is to define and study the notion of a quantum vertex operator algebra in the setting of the formal deformation theory and give interesting examples of such algebras. In particular, we construct a quantum vertex operator algebra from a rational, trigonometric, or elliptic R-matrix, which is a quantum deformation of the affine vertex operator algebra. The simplest vertex operator in this algebra is the quantum current of Reshetikhin and Semenov-Tian-Shansky.

2018

Let A be a unital algebra, δ be a linear mapping from A into itself and m, n be fixed integers. We call δ an (m, n)-derivable mapping at Z, if mδ(AB)+nδ(BA) = mδ(A)B+mAδ(B)+nδ(B)A+nBδ(A) for all A,B ∈ A with AB = Z. In this paper, (m, n)-derivable mappings at 0 (resp. IA⊕0, I) on generalized matrix algebras are characterized. We also study (m, n)-derivable mappings at 0 on CSL algebras. We reveal the relationship between this kind of mappings with Lie derivations, Jordan derivations and derivations.

1997

This paper is a continuation of "Quantization of Lie bialgebras, I" (q-alg/9606005). We show that the quantization procedure defined in "Quantization of Lie bialgebras, I" is given by universal acyclic formulas and defines a functor from the category of Lie bialgebras to the category of quantized universal enveloping algebras. We also show that this functor defines an equivalence between the category of Lie bialgebras over k[[h]] and the category quantized universal enveloping (QUE) algebras

Cornell University - arXiv, 2022

In this paper, we study the generalized derivation of a Lie subalgebra of the Lie algebra of polynomial vector fields on R n , containing all constant vector fields and the Euler vector field, under some conditions on this Lie subalgebra.

2021

In this paper, we study 3-Lie algebras with derivations. We call the pair consisting of a 3-Lie algebra and a distinguished derivation by the 3-LieDer pair. We define a cohomology theory for 3-LieDer pair with coefficients in a representation. We study central extensions of a 3-LieDer pair and show that central extensions are classified by the second cohomology of the 3-LieDer pair with coefficients in the trivial representation. We generalize Gerstenhaber’s formal deformation theory to 3-LieDer pairs in which we deform both the 3-Lie bracket and the distinguished derivation.

IRJET, 2020

We prove that the Lie Product [f1, f2] ∈ GD(L), the set of all generalized derivations on an arbitrary Lie algebra L over a fixed field K. We also show that inner derivations fa form an Ideal in derivation Algebra D(L). To this result, Jacobson [2] proposition 2 page 10 comes out as a corollary. Also we show that f1f2 may be the generalized derivation iff f1 and f2 have some possibilities.

Selecta Mathematica, 1996

In the paper [Dr3] V.Drinfeld formulated a number of problems in quantum group theory. In particular, he raised the question about the existence of a universal quantization for Lie bialgebras, which arose from the problem of quantization of Poisson Lie groups. When the paper [KL] appeared Drinfeld asked whether the methods of [KL] could be useful for the problem of universal quantization of Lie bialgebras. This paper gives a positive answer to a number of Drinfeld's questions, using the methods and ideas of [KL]. In particular, we show the existence of a universal quantization. We plan to provide positive answers to most of the remaining questions in [Dr3] in the following papers of this series.

Cornell University - arXiv, 2012

Let A be a unital algebra, δ be a linear mapping from A into itself and m, n be fixed integers. We call δ an (m, n)-derivable mapping at Z, if mδ(AB) + nδ(BA) = mδ(A)B + mAδ(B) + nδ(B)A + nBδ(A) for all A, B ∈ A with AB = Z. In this paper, (m, n)-derivable mappings at 0 (resp. IA ⊕ 0, I) on generalized matrix algebras are characterized. We also study (m, n)-derivable mappings at 0 on CSL algebras. We reveal the relationship between this kind of mappings with Lie derivations, Jordan derivations and derivations.

The authors exhibit a natural homomorphism from the algebra of quantisable forms to the Frölicher-Nijenhuis algebra of tangent valued forms on the spacetime. Quantisable forms are defined to be forms on the 1-jet space of spacetime whose Hamiltonian lift is a tangent valuable form projectable on spacetime, they constitute a graded Lie algebra with respect to a natural bracket.