Realization of infinite dimensional Lie-admissible algebras

Conference · Sat Dec 01 04:00:00 EST 1979 · Hadronic J.; (United States)

OSTI ID:6484308

Llamed, Y

Let V be the vector space, over a field F, spanned by the n nomials that are the permutations of the factors of the monomial x/sub 1/x/sub 2/...x/sub n/, and let V = V/sub 1/ + V/sub 2/ +...(direct sum). Let V+ and V/sup -/ be respectively the vector subspaces of V of completely symmetric and skew symmetric polynomials. For f/sub m/ in V/sub m and g/sub n/ in V/sub n/let f/sub m/og/sub n/ in V/sub m +n-1/ be defined by where S is a given subset of the group of permutations on 1,2,..., m+n-1 and a/sub 1/, a/sub 2/,... is a given sequence in F. The vector space V with the composition law o is an infinite dimensional nonassociative algebra, (V,o), whose structure is dependent on the given set S and sequence a/sub 1/, a/sub 2/,.... We have given examples of (V,o)-algebras that are Lie and graded Lie-admissible algebras. We have also explicitly calculated the structure constants of a (V/sup +/,o) and a (V/sup -/,o) Lie-admissible algebra; the Lie algebras associated to these algebras are infinite dimensional Witt Lie-algebras that appear in the physics of elementary particles as subalgebras of string algebras.

• Research Organization: Soreq Nuclear Research Center, Yavne, Israel
• OSTI ID: 6484308
• Report Number(s): CONF-7908175-
• Conference Information: Journal Name: Hadronic J.; (United States) Journal Volume: 3:1
• Country of Publication: United States
• Language: English

Related Subjects

658000* -- Mathematical Physics-- (-1987)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALGEBRA
GRADED LIE GROUPS
LIE GROUPS
MATHEMATICS
SYMMETRY GROUPS
TENSORS
VECTORS