A non-Lie algebraic framework and its possible merits for symmetry descriptions

Journal Article · Wed Oct 01 04:00:00 EDT 1975 · J. Math. Phys. (N.Y.), v. 16, no. 10, pp. 2130-2141

DOI:https://doi.org/10.1063/1.522447· OSTI ID:4158415

Ktorides, C N

A nonassociative algebraic construction is introduced which bears a relation to a Lie algebra L paralleling the relation between an associative enveloping algebra and L. The key ingredient of this algebraic construction is the presence of two parameters which relate it to the enveloping algebra of L. The analog of the Poincare--Birkhoff--Witt theorem is proved for the new algebra. Possibilities of physical relevance are also considered. It is noted that, if fully developed, the mathematical framework suggested by this new algebra should be non-Lie. Subsequently, a certain scheme resulting from specific considerations connected with this (non-Lie) algebraic structure is found to bear striking resemblance to a recent phenomenological theory proposed for explaining CP violation by the K$sup 0$ system. Some relevant speculations are also made in view of certain recent trends of thought in elementary particle physics. Finally, in an appendix, a Gell-Mann--Okubo-like mass formula for the new algebra is derived for an SU (3) octet.

• Research Organization: International Centre for Theoretical Physics, Trieste, Italy
• Sponsoring Organization: USDOE
• NSA Number: NSA-33-002036
• OSTI ID: 4158415
• Journal Information: J. Math. Phys. (N.Y.), v. 16, no. 10, pp. 2130-2141, Journal Name: J. Math. Phys. (N.Y.), v. 16, no. 10, pp. 2130-2141; ISSN JMAPA
• Country of Publication: United States
• Language: English

Related Subjects

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