Central extensions of generalized orthosymplectic Lie superalgebras

@article{Chang2015CentralEO,
  title={Central extensions of generalized orthosymplectic Lie superalgebras},
  author={Zhihua Chang and Yongjie Wang},
  journal={Science China Mathematics},
  year={2015},
  volume={60},
  pages={223-260}
}
We completely determine the universal central extension of the generalized orthosymplectic Lie superalgebra ospm|2n(R,-) that is coordinatized by an arbitrary unital associative superalgebra (R,-) with superinvolution. As a result, an identification between the second homology group of the Lie superalgebra ospm|2n(R,-) and the first skew-dihedral homology group of the associative superalgebra (R,-) with superinvolution is created for positive integers m and n with (m,n) ≠ (1,1) and (m, n) ≠ (2… 
View on Springer
arxiv.org
2 Citations

2 Citations

Second homology of generalized periplectic Lie superalgebras

Remarks on the second homology groups of queer Lie superalgebras

Abstract The aim of this note is to completely determine the second homology group of the special queer Lie superalgebra coordinatized by a unital associative superalgebra R, which will be achieved…

References

SHOWING 1-10 OF 24 REFERENCES

Primitive Superalgebras with Superinvolution

Abstract Our main purpose is to provide for primitive associative superalgebras a structure theory analogous to that for algebras [ 5 , 6 , 10 ] and to classify primitive superrings with…

Cohomology of Lie superalgebras and their generalizations

The cohomology groups of Lie superalgebras and, more generally, of e Lie algebras, are introduced and investigated. The main emphasis is on the case where the module of coefficients is nontrivial.…

Central extensions of Lie superalgebras

Abstract. For a commutative algebra A over a commutative ring k satisfying certain conditions, we construct the universal central extension of $ {\frak g}_k \otimes_k A $, regarded as a Lie…

Universal central extensions of slm|n over Z/2Z-graded algebras

An Introduction to Universal Central Extensions of Lie Superalgebras

We provide an introduction to the theory of universal central extensions of Lie superalgebras. In particular, we show that a Lie superalgebra has a universal central extension if and only if it is…

Central Extensions of Matrix Lie Superalgebras Over Z / 2 Z -graded Algebras

We study central extensions of the Lie superalgebra sl n ( A ) when A is a Z / 2 Z -graded superalgebra over a commutative ring K . Steinberg Lie superalgebras and their central extensions play an…

Lie Superalgebras Graded by the Root Systems C(n), D(m, n), D(2, 1, α), F(4), G(3)

Abstract We determine the Lie superalgebras that are graded by the root systems of the basic classical simple Lie superalgebras of type $C\left( n \right),D\left( m,n \right),D\left( 2,1;\alpha…

Central Extensions of Matrix Lie Superalgebras Over $\mathbb{Z}/2\mathbb{Z}$-graded Algebras

We study central extensions of the Lie superalgebra $\mathfrak{s}\mathfrak{l}_n(A)$ when A is a ℤ/2ℤ-graded superalgebra over a commutative ring K. Steinberg Lie superalgebras and their central…

Lie superalgebras graded by the root system B(m,n)

AbstractWe determine the Lie superalgebras that are graded by the root system B(m,n) of the orthosymplectic Lie superalgebra osp(2m + 1,2n).

Second homology of Lie superalgebras

The second homology of Lie superalgebras over a field of characteristic 0 extended over a supercommutative superalgebra A and their twisted version are obtained. (© 2005 WILEY‐VCH Verlag GmbH & Co.…