Degeneracy and Decomposability in Abelian Crossed Products
نویسنده
چکیده
Let p be an odd prime. In this paper we study the relationship between degeneracy and decomposability in abelian crossed products. In particular we construct an indecomposable abelian crossed product division algebra of exponent p and index p. The algebra we construct is generic in the sense of [AS78] and has the property that its underlying abelian crossed product is a decomposable division algebra defined by a non-degenerate matrix. This algebra also gives an example of an indecomposable generic abelian crossed product which is shown to be indecomposable without using torsion in the Chow group of the corresponding Severi-Brauer variety as was needed in [Kar98] and [McK08].
منابع مشابه
Indecomposable p-algebras and Galois subfields in generic abelian crossed products
Let F be a Henselian valued field with char(F ) = p and D a semi-ramified, “not strongly degenerate” p-algebra. We show that all Galois subfields of D are inertial. Using this as a tool we study generic abelian crossed product p-algebras, proving among other things that the noncyclic generic abelian crossed product p-algebras defined by non-degenerate matrices are indecomposable p-algebras. To ...
متن کاملThe non-abelian tensor product of normal crossed submodules of groups
In this article, the notions of non-abelian tensor and exterior products of two normal crossed submodules of a given crossed module of groups are introduced and some of their basic properties are established. In particular, we investigate some common properties between normal crossed modules and their tensor products, and present some bounds on the nilpotency class and solvability length of the...
متن کاملOn crossed products of the Cuntz algebra O∞ by quasi-free actions of abelian groups
We investigate the structures of crossed products of the Cuntz algebra O∞ by quasi-free actions of abelian groups. We completely determine their ideal structures and compute the strong Connes spectra and K-groups.
متن کاملThe ideal structures of crossed products of Cuntz algebras by quasi-free actions of abelian groups
We completely determine the ideal structures of the crossed products of Cuntz algebras by quasi-free actions of abelian groups and give another proof of A. Kishimoto’s result on the simplicity of such crossed products. We also give a necessary and sufficient condition that our algebras become primitive, and compute the Connes spectra and K-groups of our algebras.
متن کاملPairings from a tensor product point of view
Pairings are particular bilinear maps, and as any bilinear maps they factor through the tensor product as group homomorphisms. Besides, nothing seems to prevent us to construct pairings on other abelian groups than elliptic curves or more general abelian varieties. The point of view adopted in this contribution is based on these two observations. Thus we present an elliptic curve free study of ...
متن کامل