Related papers: Note on Centrally Extended su(2/2) and Serre Relat…
We derive the Serre relations for the generators of the quantum loop algebra L(sl_2) of the superintegrable tau_2 model in Q not 0 sectors, thus proving a fundamental conjecture in an earlier paper on the superintegrable chiral Potts model.
An analogue of Serre's theorem is established for finite dimensional simple Lie superalgebras, which describes presentations in terms of Chevalley generators and Serre type relations relative to all possible choices of Borel subalgebras.…
Over algebraically closed fields of positive characteristic, for simple Lie (super)algebras, and certain Lie (super)algebras close to simple ones, with symmetric root systems (such that for each root, there is minus it of the same…
We completely describe presentations of Lie superalgebras with Cartan matrix if they are simple Z-graded of polynomial growth. Such matrices can be neither integer nor symmetrizable. There are non-Serre relations encountered. In certain…
We discuss the possibility of a central extension of the Poincar\'e algebra and the scaling Poincar\'e algebra. In more than two space-time dimensions, all the central extensions are trivial and can be removed. In two space-time dimensions,…
The most general possible central extensions of two whole families of Lie algebras, which can be obtained by contracting the special pseudo-unitary algebras su(p,q) of the Cartan series A_l and the pseudo-unitary algebras u(p,q), are…
We construct some canonically defined central extensions of groups of symplectomorphisms. We show that this central extension is nontrivial in the case of a torus of dimension $\ge 6$ and in the case of a two-dimensional surface of genus…
We determine the central extensions of a whole family of Lie algebras, obtained by the method of graded contractions from so(N+1), N arbitrary. All the inhomogeneous orthogonal and pseudo-orthogonal algebras are members of this family, as…
We consider Borcherds superalgebras obtained from semisimple finite-dimensional Lie algebras by adding an odd null root to the simple roots. The additional Serre relations can be expressed in a covariant way. The spectrum of generators at…
The arising of central extensions is discussed in two contexts. At first classical counterparts of quantum anomalies (deserving being named as "classical anomalies") are associated with a peculiar subclass of the non-equivariant maps.…
We study the central extensions of Lie algebras graded by an irreducible locally finite root system.
A Lie (super)algebra with a non-degenerate invariant symmetric bilinear form will be called a NIS-Lie (super)algebra. The double extension of a NIS-Lie (super)algebra is the result of simultaneously adding to it a central element and an…
Some properties of central extensions of 2+1 dimensional Galilei group are discussed. It is shown that certain families of extensions are isomorphic. An interpretation of new nontrivial cocycle is offered. A few bibliographical remarks are…
In this paper, using a quantum superalgebra associated with the universal central extension of sl(2,2)^{(1)}, we introduce new R-matrices having an extra parameter x. As x\to 0, they become those associated with the symmetric and…
The central extension of a new infinite dimensional algebra which has both $W_\infty$ and affine $sl(2,R)$ as subalgebras is found. The critical dimension of the corresponding string model is $D=5$.
We construct a central extension of the smooth Deligne cohomology group of a compact oriented odd dimensional smooth manifold, generalizing that of the loop group of the circle. While the central extension turns out to be trivial for a…
Dialgebras are generalizations of associative algebras which give rise to Leibniz algebras instead of Lie algebras. In this paper we study super dialgebras and Leibniz superalgebras, which are $\z_2$-graded dialgebras and Leibniz algebras.…
We investigate the integrable structure of spin chain models with centrally extended su(2|2) and psu(2,2|4) symmetry. These chains have their origin in the planar AdS/CFT correspondence, but they also contain the one-dimensional Hubbard…
Restricted Heisenberg Lie superalgebras are studied over an algebraically closed field F of characteristic p > 2. We use the ordinary 1- and 2-cohomology spaces with trivial coefficients to compute the restricted 2-cohomology spaces. As an…
Suppose the ground field is algebraically closed and of characteristic different from 2. In this paper, we described the intrinsic connections among linear super-commuting maps, super-biderivations and centroids for Lie superalgebras…