Forms over semisimple algebras with involution
نویسندگان
چکیده
منابع مشابه
Sesquilinear forms over rings with involution
Many classical results concerning quadratic forms have been extended to Hermitian forms over algebras with involution. However, not much is known in the case of sesquilinear formswithout any symmetry property. The present paperwill establish aWitt cancellation result, an analogue of Springer’s theorem, as well as some local–global and finiteness results in this context. © 2013 Elsevier B.V. All...
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 کاملLecture 5: Semisimple Lie Algebras over C
In this lecture I will explain the classification of finite dimensional semisimple Lie algebras over C. Semisimple Lie algebras are defined similarly to semisimple finite dimensional associative algebras but are far more interesting and rich. The classification reduces to that of simple Lie algebras (i.e., Lie algebras with non-zero bracket and no proper ideals). The classification (initially d...
متن کاملNormed algebras with involution
We show that most of the theory of Hermitian Banach algebras can be proved for normed ∗-algebras without the assumption of completeness. The condition r(x) ≤ p(x) for all x (where p(x) = r(x∗x)1/2 is the Pták function), which is essential in the theory of Hermitian Banach algebras, is replaced for normed ∗-algebras by the condition r(x + y) ≤ p(x) + p(y) for all x, y. In case of Banach ∗-algebr...
متن کاملReal Representations of Semisimple Lie Algebras Have Q-forms
We prove tha t each real semisimple Lie algebra g has a Q-form go, such that every real representation of go can be realized over Q. This was previously proved by M. S. Raghunathan (and rediscovered by P. Eberlein) in the special case where g is compact.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1969
ISSN: 0021-8693
DOI: 10.1016/0021-8693(69)90019-2