History and methods of Lie-admissible algebras

Conference · Mon Feb 01 04:00:00 EST 1982 · Hadronic J.; (United States)

OSTI ID:6934997

Tomber, M L

The condition that an algebra be Lie-admissible is weak and some strong, additional assumptions were made such as U is flexible (x(yx) = (xy)x, x,y element of U) and U/sup -/ is a simple Lie algebra. For any algebra, the mappings R/sub x/: y ..-->.. yx and L/sub x/: y ..-->.. xy are linear transformations on the vector space of U. A flexible Lie-admissible algebra satisfies the condition: (yz) (R/sub x/ - L/sub x/) = y(R/sub x/ - L/sub x/)z + y(z(R/sub x/ - L/sub x/)). Thus R/sub x/ - L/sub x/ is a derivation on U. In a Lie algebra the mapping ad/sub x/ has the same property. This suggests the possibility of using for Lie-admissible algebras methods similar to those used for Lie algebras. It has been suggested that physical applications would demand a derivative property or that flexible Lie-admissible algebras are appropriate algebras for physics. Gradually it has been possible to relax some of the other assumptions. This progress towards a structure and classification theory has been achieved by using our extensive knowledge of Lie algebras and their representations. Beginning in 1967, R.M. Santilli suggested other approaches to Lie-admissible algebra.

• Research Organization: Michigan State Univ., East Lansing
• OSTI ID: 6934997
• Report Number(s): CONF-820136-
• Conference Information: Journal Name: Hadronic J.; (United States) Journal Volume: 5:2
• Country of Publication: United States
• Language: English

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