# 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…

## 2 Citations

### Second homology of generalized periplectic Lie superalgebras

- MathematicsLinear Algebra and its Applications
- 2018

### Remarks on the second homology groups of queer Lie superalgebras

- MathematicsCommunications in Algebra
- 2021

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

- Mathematics
- 1998

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

- Mathematics
- 1998

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

- Mathematics
- 2001

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…

### An Introduction to Universal Central Extensions of Lie Superalgebras

- Mathematics
- 2003

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

- Mathematics
- 2011

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)

- MathematicsCanadian Mathematical Bulletin
- 2002

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

- Mathematics
- 2013

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)

- Mathematics
- 2002

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

- Mathematics, Chemistry
- 2005

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.…