Some identities valid in special Jordan algebras but not valid in all Jordan algebras
نویسندگان
چکیده
منابع مشابه
Special Identities for Quasi-jordan Algebras
Semispecial quasi-Jordan algebras (also called Jordan dialgebras) are defined by the polynomial identities a(bc) = a(cb), (ba)a = (ba)a, (b, a, c) = 2(b, a, c)a. These identities are satisfied by the product ab = a a b + b ` a in an associative dialgebra. We use computer algebra to show that every identity for this product in degree ≤ 7 is a consequence of the three identities in degree ≤ 4, bu...
متن کاملJordan algebras and Capelli identities
The purpose of this paper is to establish a connection between semisimple Jordan algebras and certain invariant differential operators on symmetric spaces; and to prove an identity for such operators which generalizes the classical Capelli identity. The norm function on a simple real Jordan algebra gives rise to invariant differential operators Dm on a certain symmetric space which is a natural...
متن کاملApproximation of Jordan homomorphisms in Jordan Banach algebras RETRACTED PAPER
In this paper, we investigate the generalized Hyers-Ulam stability of Jordan homomorphisms in Jordan Banach algebras for the functional equation begin{align*} sum_{k=2}^n sum_{i_1=2}^ksum_{i_2=i_{1}+1}^{k+1}cdotssum_{i_n-k+1=i_{n-k}+1}^n fleft(sum_{i=1,i not=i_{1},cdots ,i_{n-k+1}}^n x_{i}-sum_{r=1}^{n-k+1} x_{i_{r}}right) + fleft(sum_{i=1}^{n}x_{i}right)-2^{n-1} f(x_{1}) =0, end{align*} where ...
متن کاملHom-alternative Algebras and Hom-jordan Algebras
The purpose of this paper is to introduce Hom-alternative algebras and Hom-Jordan algebras. We discuss some of their properties and provide construction procedures using ordinary alternative algebras or Jordan algebras. Also, we show that a polarization of Hom-associative algebra leads to Hom-Jordan algebra. INTRODUCTION Hom-algebraic structures are algebras where the identities defining the st...
متن کاملSimple Conformal Algebras Generated by Jordan Algebras
1 Background and Motivation We start with an example of affine Kac-Moody algebras and the Virasoro algebra. In this talk, F will be a field with characteristic 0, and all the vector spaces are assumed over F. Denote by Z the ring of integers and by N the set of nonnegative integers. Let 2 ≤ n ∈ N. Set sl(n,F) = {A ∈ Mn×n(F) | tr A = 0}, (1.1) 〈A,B〉 = tr AB for A,B ∈ sl(n,F), (1.2) where Mn×n(F)...
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: Pacific Journal of Mathematics
سال: 1966
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1966.16.47