# Finite-dimensional simple modular Lie superalgebra â„³

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We classify the anti-involutions of the superalgebra of quantum pseudodifferential operators on the super circle S1âˆ£1 preserving the principal gradation, producing in this way a family of Lie subalgebras minus fixed by these anti-involutions. We classify the irreducible quasifinite highest...

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In this article, it is proved that the invariant consisting of the scaled ordered K-group and the space of tracial states, together with the natural pairing between them, is a complete invariant for the class of unital simple C *-algebras which can be expressed as the inductive limit of a...

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This paper is devoted to counting the number of isomorphism classes of pointed hyperelliptic curves over finite fields. We deal with the genus 4 case and the finite fields are of even characteristics. The number of isomorphism classes is computed and the explicit formulae are given. This number...

- Periodic Groups Saturated with Finite Simple Groups of Types U and L. Lytkina, D.; Shlepkin, A. // Algebra & Logic;Sep2016, Vol. 55 Issue 4, p289
Suppose that $$ \mathfrak{M} $$ is a set whose elements are simple three-dimensional unitary groups U ( q) and linear groups L ( q) over finite fields. We prove that a periodic group saturated with groups of $$ \mathfrak{M} $$ is locally finite and isomorphic to U ( Q) or L ( Q) for some locally...

- Matrix elements and duality for type 2 unitary representations of the Lie superalgebra gl(m|n). Werry, Jason L.; Gould, Mark D.; Isaac, Phillip S. // Journal of Mathematical Physics;2015, Vol. 56 Issue 12, p1
The characteristic identity formalism discussed in our recent articles is further utilized to derive matrix elements of type 2 unitary irreducible gl(m|n) modules. In particular, we give matrix element formulae for all gl(m|n) generators, including the non-elementary generators, together with...

- The central closure of the simple “strange” lie superalgebras extended over a commutative algebra. Mikhalev, A. V.; Pinchuk, I. A. // Journal of Mathematical Sciences;Jun2006, Vol. 135 Issue 5, p3350
In this work we study central extensions of Lie superalgebras g( A), where g = P( n âˆ’ 1) are simple Lie superalgebras from one of the so-called â€œstrangeâ€ series. We show that universal central extensions of these Lie superalgebras ara trivial, i.e., they are isomorphic to the...

- Low Dimensional Homology Groups of the Orthosymplectic Lie Superalgebra osp(1, 2). Biyogmam, Guy Roger // European Journal of Pure & Applied Mathematics;2014, Vol. 7 Issue 4, p395
We realize the Lie superalgebra osp(1, 2) in terms of first order differential operators and endow it with the Lie superbracket of vector fields to determine the basis (co)cycles of low dimensional (co)homology groups of osp(1, 2) with trivial coefficients, using the complex introduced by Tanaka...

- The unit group of FS 4. Khan, M.; Sharma, R.K.; Srivastava, J.B. // Acta Mathematica Hungarica;Jan2008, Vol. 118 Issue 1/2, p105
A complete characterization is given for the unit group U( FS 4) of the group algebra FS 4 of the symmetric group S 4 of degree 4 over a finite field F.

- SEMIFIELDS AS FREE MODULES1. Al-Ali, Mashhour I. // Quarterly Journal of Mathematics;Mar2011, Vol. 62 Issue 1, p1
The aim of this paper is to prove that, if S is a finite semifield over a finite field, and E is an elementary abelian 2-group of automorphisms, then E acts freely on S. Moreover, if E acts freely of rank 1 and if S has even order, then |E| â‰¤ 4.