Involutions and anti-automorphisms of central simple algebras

Graded Algebras, Anti-involutions, Simple Groups and Symmetric Spaces

Essential Dimension of Simple Algebras with Involutions

Let 1 ≤ m ≤ n be integers with m|n and Alg n,m the class of central simple algebras of degree n and exponent dividing m. In this paper, we find upper bounds for the essential (2)-dimension of Alg n,2 . Moreover, we find a stronger upper bound for the essential 2-dimension of Alg n,2 over a field F of char(F ) 6= 2. As a result, we show that ed2(Alg16,2) = 24 over a field F of char(F ) 6= 2.

Torsion automorphisms of simple Lie algebras

An automorphism σ of a simple finite dimensional complex Lie algebra g is called torsion, if σ has finite order in the group Aut(g) of all automorphisms of g. The torsion automorphisms of g were classified by Victor Kac in [12], as an application of his results on infinite dimensional Lie algebras. Those torsion automorphisms contained in the identity component G = Aut(g)◦ are called inner; the...

Central Simple Poisson Algebras

In this paper, we determine the isomorphism classes of the central simple Poisson algebras introduced earlier by the second author. The Lie algebra structures of these Poisson algebras are in general not finitely-graded.

Algebras and Involutions

• Vectorspaces over division rings • Matrices, opposite rings • Semi-simple modules and rings • Semi-simple algebras • Reduced trace and norm • Other criteria for simplicity • Involutions • Brauer group of a field • Tensor products of fields • Crossed product construction of simple algebras • Cyclic algebra construction of simple algebras • Quaternion algebras • Examples • Unramified extensions...