A *- vector space is a pair (V, *) consisting of a vector space V and a map *: V ? V: x a*x, x ? V, with the properties: **x = x, *()xy+ = **xy+, ** (λ x) = λ x , x, y V, λ C (linear involution or vector space involution). A * - algebra (or involutive algebra) is a * - vector space (A, *) whose involution satisfies the additional property: ???***(),,xyyxxy?=??V (algebraic involution of the algebra A). Here the following questions arise: Question 1: Can we find all (: linear) involutions of a given vector space V? Question 2: Can we find all (algebraic) involutions of a given algebra A? Question 3: Can we find all multiplications of a vector space V and, in particular, the associative ones? In this paper we answer in the positive the first and third question, while we give a relevant hint (cf. Theorem 1.3), concerning the second one.

Στοιχεία Άρθρου

Περιοδικό	Δελτίο της Ελληνικής Μαθηματικής Εταιρίας
Αρ. Τεύχους	Τεύχος 44
Περίοδος	2000
Συγγραφέας	Yannis Tsertos
Αρ. Αρθρου	15
Σελίδες	143-155
Γλώσσα	-
Λέξεις Κλειδιά	involution, vector algebra, vector space

Involutions of Vector spaces and Algebras