Maximal subalgebras of Jordan superalgebras

The maximal subalgebras of the finite-dimensional simple special Jordan superalgebras over an algebraically closed field of characteristic 0 are studied. This is a continuation of a previous paper by the same authors about maximal subalgebras of simple associative superalgebras, which is instrumental here.     

On herstein's constructions relating jordan and associative superalgebras

We investigate the Jordan structure of a prime associative superalgebra and the Jordan structure of the symmetric elements of a *-prime associative superalgebra with superinvolution.     

Engel’s theorem for malcev superalgebras

A version of Engel’s theorem for Malcev superalgebras is proved in the spirit of theJacobson-Engel theorem for Lie algebras. Some consequences for the structure of Malcev superalgebras with trivial Lie nucleus are derived.     

Simple finite-dimensional modular noncommutative Jordan superalgebras

We classify the central simple finite-dimensional noncommutative Jordan superalgebras over an algebraically closed field of characteristic $p>2$. The case of characteristic 0 was considered by the authors in the previous paper [21]. In particular, we describe Leibniz brackets on all finite dimensional central simple Jordan superalgebras except mixed (nor vector neither Poisson) Kantor doubles of the supercommutative superalgebra $B(m,n)$.     

Quaternions,octonions and the forms of the exceptional simple classical Lie superalgebras

The forms of the exceptional simple classical Lie superalgebras are determined over arbitrary fields of characteristic $\ne 2,3$.     

A note on bideterminants for Schur superalgebras

Let S(m|n,r)_Z be a Z-form of a Schur superalgebra S(m|n,r) generated by elements ξ_i,j. We solve a problem of Muir and describe a Z-form of a simple S(m|n,r)-module D_λ,Q over the field Q of rational numbers, under the action of S(m|n,r)_Z. This Z-form is the Z-span of modified bideterminants [T_?:T_i] defined in this work. We also prove that each [T_?:T_i] is a Z-linear combination of modified bideterminants corresponding to (m|n)-semistandard tableaux T_i.     

Quantum Schur superalgebras and Kazhdan-Lusztig combinatorics

We introduce the notion of quantum Schur (or q-Schur) superalgebras. These algebras share certain nice properties with q-Schur algebras such as the base change property, the existence of canonical Z[v,v⁻¹]-bases, the duality relation with Manin’s quantum matrix superalgebra A(m|n), and the bridging role between quantum enveloping superalgebras of gl(m|n) and the Hecke algebras of type A. We also construct a cellular -basis and determine its associated cells, called supercells, in terms of a Robinson-Schensted-Knuth supercorrespondence. In this way, we classify all irreducible representations over via supercell modules.     

Lie superalgebras graded by the root system B(<Emphasis Type="Italic">m,n</Emphasis>)

We determine the Lie superalgebras that are graded by the root system B(m,n) of the orthosymplectic Lie superalgebra osp(2m + 1,2n). Mathematics Subject Classification (2000) Primary 17B70, Secondary 17A70     

The shape preserving ang high accuracy approximation with multiquadric

This paper discusses the sufficient conditions for the shape preserving quasi-interpolation with multiquadric. Some quasi-interpolation schema is given such that the interpolation as well as its high derivatives is convergent. Supported by the National Natural Science Foundation of China.     

On the lie structure of the skew elements of a prime superalgebra with superinvolution

We investigate the Lie structure of the Lie superalgebra K of skew elements of a prime associative superalgebra A with superinvolution. It is proved that if A is not a central order in a Clifford superalgebra of dimension at most 16 over the center then any Lie ideal of K or [K,K] contains[J ∩K,K] for some nonzero ideal J of A or is contained in the even part of the center of A.     

Monotonicity preserving representations of non-polynomial surfaces

We prove that, in contrast to the case for rational surfaces, some tensor product representations through spaces containing algebraic, trigonometric and hyperbolic polynomials are monotonicity preserving. The surface representations provided in this paper are the only known monotonicity preserving surfaces in addition to the tensor product Bézier and tensor product B-spline surfaces.     

Howe duality and combinatorial character formula for orthosymplectic Lie superalgebras

We study the Howe dualities involving the reductive dual pairs (O(d),spo(2m|2n)) and (Sp(d),osp(2m|2n)) on the (super)symmetric tensor of . We obtain complete decompositions of this space with respect to their respective joint actions. We also use these dualities to derive a character formula for these irreducible representations of spo(2m|2n) and osp(2m|2n) that appear in these decompositions.     

Skew-symmetric identities of octonions

Quadratic alternative superalgebras are introduced and their super-identities and central functions on one odd generator are described. As a corollary, all multilinear skew-symmetric identities and central polynomials of octonions are classified.     

Group gradings on the superalgebras M(m,n), A(m,n) and P(n)

We classify gradings by arbitrary abelian groups on the classical simple Lie superalgebras $P(n)$, $n\ge 2$, and on the simple associative superalgebras $M(m,n)$, $m,n\ge 1$, over an algebraically closed field: fine gradings up to equivalence and G-gradings, for a fixed group G, up to isomorphism. As a corollary, we also classify up to isomorphism the G-gradings on the classical Lie superalgebra $A(m,n)$ that are induced from G-gradings on $M(m+1,n+1)$. In the case of Lie superalgebras, the characteristic is assumed to be 0.     

Topological and bornological characterisations of ideals in von Neumann algebras: II

SupposeM is a von Neumann algebra on a Hilbert spaceH andI is any norm closed ideal inM. We extend to this setting the well known fact that the compact operators on a Hilbert space are precisely those whose restrictions to the closed unit ball are weak to norm continuous.