منابع مشابه
Scaled trace forms of central simple algebras
Any central simple algebra over a field of characteristic not two has a well-defined non-singular quadratic form called the trace form attached to it. This quadratic form was studied in [6] from the viewpoint of the algebraic theory of quadratic forms. In this article we examine a generalization of trace forms to “scaled trace forms” which are defined via the reduced trace map together with sca...
متن کاملOn the computation of trace forms of algebras with involution
Definitions and notation: Let A be a central simple algebra of degree n over a field k of characteristic different from 2. An involution on A is a ring antiautomorphism of order at most 2. An involution σ is of the first kind if σ|k = Idk, and of the second kind if σ|k is a non trivial involution on k, denoted by .̄ In the last case, k is a quadratic extension of the subfield k0 fixed by .̄ So we...
متن کاملHigher Trace Forms and Essential Dimension in Central Simple Algebras
We show that the essential dimension of a finite-dimensional central simple algebra coincides with the essential dimension of its rlinear trace form, (a1, . . . , ar) 7→ tr(a1 . . . ar), for any r ≥ 3.
متن کاملamenability of banach algebras
chapters 1 and 2 establish the basic theory of amenability of topological groups and amenability of banach algebras. also we prove that. if g is a topological group, then r (wluc (g)) (resp. r (luc (g))) if and only if there exists a mean m on wluc (g) (resp. luc (g)) such that for every wluc (g) (resp. every luc (g)) and every element d of a dense subset d od g, m (r)m (f) holds. chapter 3 inv...
15 صفحه اولSome properties of the symbol algebras
algebra. First, we recall some definitions in the theory of associative algebras. LetA 6= 0 be an algebra over the fieldK. If the equations ax = b, ya = b, ∀a, b ∈ A, a 6= 0, have unique solutions, then the algebra A is called a division algebra. If A is a finite-dimensional algebra, then A is a division algebra if and only if A is without zero divisors (x 6= 0, y 6= 0 ⇒ xy 6= 0).(see [9]) Let ...
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ژورنال
عنوان ژورنال: Algebra Colloquium
سال: 2012
ISSN: 1005-3867,0219-1733
DOI: 10.1142/s1005386712000892