Yangian of the Strange Lie Superalgebra of Q n-1 Type, Drinfel'd Approach (original) (raw)

The Yangian of the strange Lie superalgebra and its quantum double

Theoretical and Mathematical Physics, 2013

We construct the Yangian of the strange Lie superalgebra as a particular case of the general construction of a twisted Yangian. We describe a Poincaré-Birkhoff-Witt basis of the Yangian of the type-Qn Lie superalgebra and construct the quantum double of the Yangian of the type-Q2 strange Lie superalgebra.

Yangians of classical Lie superalgebras: basic constructions, quantum double and universal R-matrix

Some basic results of the theory of Yangians of Lie superalgebras are described. Yangian of basic Lie superalgebra is described as a result of quantization of Lie superbialgebra of polynomial loops. Also, we consider a quantization of Lie superalgebra of twisted currents. Two systems of generators and defining relations are introduced. Equivalence of this systems of generators and defining relations is proved. The notion of double of Yangian and formula for universal R-matrix for double of Yangian are discussed for Yangian of Lie superalgebra A(m, n) type.

Drinfeld Yangian of the queer Lie superalgebra sq 1

Journal of Physics: Conference Series, 2019

Drinfeld Yangian of a queer Lie superalgebra sq1 is defined as the quantization of a Lie bisuperelgebra of twisted polynomial currents. An analogue of the new system of generators of Drinfeld is being constructed. It is proved for the case Lie superalgebra sq1 that this so defined Yangian and the Yangian, introduced earlier by M. Nazarov using the Faddeev-Reshetikhin-Takhtadzhjan approach, are isomorphic.

On representations of Yangian of Lie SuperalgebraA(n,n) type

Journal of Physics: Conference Series, 2013

The finite-dimensional irreducible representations of Yangian of Lie Superalgebra of A(n, n) type is described in terms of Drinfel'd polynomials. The necessarily and sufficient conditions of finite-dimensionality of irreducible representation are formulated and proved. The Poincare-Birkoff-Witt theorem for Yangian of A(n, n) Lie Superalgebra is proved also. 0 This work is partially supported by Federal Program "Scientific and scientific-educational personnel of innovative Russia event 1.2.2 (contract number P116) and by Federal Program "Scientific and scientific-educational personnel of innovative Russia"(agreement № 14.A18.

A sketch of Lie superalgebra theory

Communications in Mathematical Physics, 1977

This article deals with the structure and representations of Lie superalgebras (Z 2-graded Lie algebras). The central result is a classification of simple Lie superalgebras over IR and C.

IMPERIAL-TP-AR-2010-1 The Yangian of sl(n|m) and the Universal R-matrix

2016

In this paper we study Yangians of sl(n|m) superalgebras. We derive the universal R-matrix and evaluate it on the fundamental representation obtaining the standard Yang R-matrix with unitary dressing factors. For m = 0, we directly recover up to a CDD factor the well-known S-matrices for relativistic integrable models with su(n) symmetry. Hence, the universal R-matrix found provides an abstract plug-in formula, which leads to results obeying fundamental physical constraints: crossing symmetry, unitrarity and the Yang-Baxter equation. This implies that the Yangian double unifies all desired symmetries into one algebraic structure. In particular, our analysis is valid in the case of sl(n|n), where one has to extend the algebra by an additional generator leading to the algebra gl(n|n). We find two-parameter families of scalar factors in this case and provide a detailed study for gl(1|1).

On unitary Lie superalgebras from the spin-orbit supersymmetrisation procedure

Journal of Physics A: Mathematical and General, 1990

From the basis elements of a Clifford algebra Cl, we generate a grading leading to a unitary Lie superalgebra when n is even. Such a construction is motivated by the understanding of the specific properties of the fermionic variables in the so-called spin-orbit coupling procedure of supersymmetrisation in N = 2 supersymmetric quantum mechanics. The n-odd case is also considered and some specific examples are discussed.

Drinfeld Twists and Algebraic Bethe Ansatz of the Supersymmetric Model Associated with U q (gl(m|n))

Communications in Mathematical Physics, 2006

We construct the Drinfeld twists (or factorizing F-matrices) of the supersymmetric model associated with quantum superalgebra U q (gl(m|n)), and obtain the completely symmetric representations of the creation operators of the model in the F-basis provided by the F-matrix. As an application of our general results, we present the explicit expressions of the Bethe vectors in the F-basis for the U q (gl(2|1))-model (the quantum t-J model).

The gl (M|N) super Yangian and its finite-dimensional representations

Letters in Mathematical Physics, 1996

Methods are developed for systematically constructing the finite dimensional irreducible representations of the super Yangian Y (gl(M |N)) associated with the Lie superalgebra gl(M |N). It is also shown that every finite dimensional irreducible representation of Y (gl(M |N)) is of highest weight type, and is uniquely characterized by a highest weight. The necessary and sufficient conditions for an irrep to be finite dimensional are given.