Alternative algebras satisfying polynomial identities
نویسندگان
چکیده
منابع مشابه
Algebras, Dialgebras, and Polynomial Identities *
This is a survey of some recent developments in the theory of associative and nonassociative dialgebras, with an emphasis on polynomial identities and multilinear operations. We discuss associative, Lie, Jordan, and alternative algebras, and the corresponding dialgebras; the KP algorithm for converting identities for algebras into identities for dialgebras; the BSO algorithm for converting oper...
متن کاملColength of *-Polynomial Identities of Simple *-Algebras
We compute the sequence of colengths in the cocharacters of the ∗polynomial identities of the ∗-simple algebra M2(F )⊕M2(F ), char(F ) = 0.
متن کاملOn quantum matrix algebras satisfying the Cayley-Hamilton-Newton identities
The Cayley-Hamilton-Newton identities which generalize both the characteristic identity and the Newton relations have been recently obtained for the algebras of the RTT-type. We extend this result to a wider class of algebras M(R̂, F̂ ) defined by a pair of compatible solutions of the Yang-Baxter equation. This class includes the RTTalgebras as well as the Reflection equation algebras. On leave o...
متن کاملIsotopy and Identities in Alternative Algebras
In this paper we show how to construct an isomorphism between an alternative algebra A over a field of characteristic 6= 3 and its isotope A(1+c), where c is an element of Zhevlakov’s radical of A. This leads to the equivalence of any polynomial identity f = 0 in alternative algebras and the isotope identity f(s) = 0. Given an invertible element s of an alternative algebra A, we can form a new ...
متن کاملIdentities for the Associator in Alternative Algebras
The associator is an alternating trilinear product for any alternative algebra. We study this trilinear product in three related algebras: the associator in a free alternative algebra, the associator in the Cayley algebra, and the ternary cross product on four-dimensional space. This last example is isomorphic to the ternary subalgebra of the Cayley algebra which is spanned by the non-quaternio...
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: 1973
ISSN: 0021-8693
DOI: 10.1016/0021-8693(73)90138-5