The Simplicity of Certain Nonassociative Algebras

The Simplicity of Certain Nonassociative

Introduction. Let V be an additively written elementary £-group of order pn, where w>l, and let (u, v), yp(u, v) he two alternate biadditive functions defined on V and with values in a field K of characteristic p. Let & be a fixed nonzero element in V, and assume that the following two conditions are satisfied: (0.1) If a, P are nonzero elements in K then a<p(u, v) +P\f/(u, v)=0 lor all v im...

Linear Factorization of Conical Polynomials over Certain Nonassociative Algebras

Conical polynomials are defined as certain polynomials in quadratic elements of the universal enveloping algebra of a semisimple symmetric Lie algebra over a field of characteristic zero. These polynomials were used in an earlier paper to describe the conical vectors in certain induced modules. Here it is shown that when the base field is extended to a certain type of nonassociative algebra, th...

Simplicity of the Reduced C-algebras of Certain Coxeter Groups

Let (G, S) be a finitely generated Coxeter group, such that the Coxeter system is indecomposable and the canonical bilinear form is indefinite but non-degenerate. We show that the reduced C∗-algebra of G is simple with unique normalised trace. For an arbitrary finitely generated Coxeter group we prove the validity of a Haagerup inequality: There exist constants C > 0 and Λ ∈ N such that for a f...

Nonassociative Algebras

On Nonassociative Division Algebras^)