We also discuss quaternion algebras over global fields and fields of Laurent series over a perfect field of characteristic $2$ and show that the quaternion algebras over these fields are determined by their separable quadratic subfields.doi:10.1016/j.jpaa.2016.05.006Adam Chapman...
Universal factorization equalities over generalized quaternion algebras A generalized quaternion algebra (u,v F) over an arbitrary field F of characteristic not two is studied [cf. T. Y. Lam, The algebraic theory of quadratic forms (1973; Zbl 0259.10019); R. S. Pierce, Associative algebras (19...
A biquaternion algebra A over a field F of characteristic different from two is a tensor product A=A 1 A 2 of two quaternion algebras A 1 and A 2 over F. The decomposition of A is unique if we fix an orthogonal involution σ of discrimin... MA Knus,TY Lam,DB Shapiro,... - Di...
Chapter 14 Quaternion algebras over global fields In this chapter, we discuss quaternion algebras over global fields and characterize them up to isomorphism. 14.1 Ramification To motivate the classification of quaternion algebras over Q, we consider by analogy a classification of quadratic fields. We ...
Central idempotents of generalized quaternion group algebras Throughout this section, the characteristic of Fq is coprime to 4n, there are irreducible factorizations of xn−1 and xn+1 over Fq as (2.1), αi denotes a root of the polynomial fi,1≤i≤r+s, βj denotes a root of the poly...
In [2], Bovdi gave a comprehensive survey of results concerning the group of units of a modular group algebra of characteristic p. There is a long tradition on the study of the unit group of finite group algebras [3], [4], [5], [6], [7], [8], [9], [10], [11], [12]....
inspace. Points in space can be represented by their coordinates, which are triples of numbers, and for many years Hamilton had known how to add and multiply triples of numbers. But he had been stuck on the problem of division: He did not know how to take the quotient of two points ...
Accept all cookies Abstract We describe the structure of the supersingular locus of a Shimura variety for a quaternionic unitary similitude group of degree 2 over a ramified odd primepif the level atpis given by a special maximal compact open subgroup. More precisely, we show that such a locus...
Let A and B denote the algebras of functions on A and B respectively. Let J⊂B be the ideal such that A=B/J. Let m⊂B be the ideal of p. Since p(n) is a closed analytic subspace of A then(4.7.4)J⊂mn+1. We have the obvious epimorphism of algebras B⟶A/(m/J)n...
We first present some results that hold for an algebraically closed field of arbitrary characteristic p>0 and principal blocks with arbitrary defect groups. Throughout this section, we assume that G and H are two arbitrary finite groups, we let P denote a common p-subgroup of G and H. ...