## 25 Citations

### Twisted fermionic and bosonic representations for a class of BC-graded Lie algebras

- Mathematics
- 2011

In this paper, we study the fermionic and bosonic representations for a class of BC-graded Lie algebras coordinatized by skew Laurent polynomial rings. This generalizes the fermionic and bosonic…

### Lie Superalgebras Arising from Bosonic Representation

- Mathematics
- 2012

A 2-toroidal Lie superalgebra is constructed using bosonic fields and a ghost field. The superalgebra contains osp(1 | 2n)(1) as a distinguished subalgebra and behaves similarly to the toroidal Lie…

### Bosonic–fermionic realizations of root spaces and bilinear forms for Lie superalgebras

- MathematicsJournal of Algebra and Its Applications
- 2019

We study bosonic–fermionic constructions of the root spaces of the orthosymplectic Lie superalgebras. We also present explicitly bosonic–fermionic realizations of the supertrace forms for the…

### Fermionic realization of toroidal Lie algebras of classical types

- Mathematics
- 2008

We use fermionic operators to construct toroidal Lie algebras of classical types, including in particular that of symplectic affine algebras, which is first realized by fermions.

### On Universal Central Extensions of sln(A)

- Mathematics

We describe the interplay between several (co)homology theories in the context of computing universal central extensions of Lie algebras of matrices over some associative algebras. We illustrate…

### Fermionic realization of twisted toroidal Lie algebras

- MathematicsJournal of Algebra and Its Applications
- 2020

In this paper, we construct a fermionic realization of the twisted toroidal Lie algebra of type [Formula: see text] and [Formula: see text] based on the newly found Moody–Rao–Yokonuma-like…

### Bosonic free field realization of twisted 2-toroidal Lie algebras

- Mathematics
- 2018

Using free fields, we construct a bosonic realization of toroidal Lie algebras of type $A_{2n-1}, A_{2n}, D_{n+1}, D_4$ which are twisted by a Dynkin diagram automorphism. This realization is based…

### Toroidal Lie superalgebras and free field representations

- Mathematics
- 2013

A loop-algebraic presentation is given for toroidal Lie superalgebras of classical types. Based on the loop superalgebra presentation free field realizations of toroidal Lie superalgebras are…

## References

SHOWING 1-10 OF 22 REFERENCES

### Bosonic and fermionic realizations of the affine algebra $$g\hat l_n $$

- Mathematics
- 1991

AbstractWe give an explicit description of all inequivalent Heisenberg subalgebras of the affine Lie algebra
$$g\hat l_n (\mathbb{C})$$
and the associated vertex operator constructions of the level…

### Two constructions of affine Lie algebra representations and boson-fermion correspondence in quantum field theory

- Mathematics
- 1981

### Bosonic and Fermionic Realizations of The Affine Algebra sˆo2n

- Mathematics
- 1992

We give an explicit description of the Kac-Peterson-Lepowsky constr tion of the basic representation for the affine Lie algebra sˆo2n(C). Using the conjugacy classes of the Weyl group of sˆo2n(C), we…

### Spin and wedge representations of infinite-dimensional Lie algebras and groups.

- MathematicsProceedings of the National Academy of Sciences of the United States of America
- 1981

A construction of all level-one highest-weight representations of orthogonal affine Lie algebras in terms of creation and annihilation operators on an infinite-dimensional Grassmann algebra is deduced.

### Infinite additional symmetries in two-dimensional conformal quantum field theory

- Mathematics
- 1985

This paper investigates additional symmetries in two-dimensional conformal field theory generated by spin s = 1/2, 1,...,3 currents. For spins s = 5/2 and s = 3, the generators of the symmetry form…

### Lie Algebras with Triangular Decompositions

- Mathematics
- 1995

Lie Algebras. Lie Algebras Admitting Triangular Decompositions. Lattices and Root Systems. Contragredient Lie Algebras. The Weyl Group and Its Geometry. Category O for Kac--Moody Algebras. Conjugacy…

### Representation Theory: A First Course

- Mathematics
- 1991

This volume represents a series of lectures which aims to introduce the beginner to the finite dimensional representations of Lie groups and Lie algebras. Following an introduction to representation…

### α-Derivations

- Canadian Mathematical Bulletin
- 1995

Abstract Let A be a commutative k-algebra with 1. We present a characterization of α-derivations, for α: A →> A a morphism of algebras, using α-Taylor series. When S = C[x,x-1,ξ] and α(x) = qx, α(ξ)…

### Spinor representations of affine Lie algebras.

- MathematicsProceedings of the National Academy of Sciences of the United States of America
- 1980

This work constructs two representations of a Lie algebra, which are called spinor representations, and obtains classical Jacobi identities and addition formulas for elliptic theta-functions for elliptical fermion fields.