Algebras of quotients of Jordan-Lie algebras. (English) Zbl 1405.17003
Summary: In this article, we introduce the notion of algebra of quotients of a Jordan-Lie algebra. Properties such as semiprimeness or primeness can be lifted from a Jordan-Lie algebra to its algebras of quotients. Finally, we construct a maximal algebra of quotients for every semiprime Jordan-Lie algebra.
MSC:
| 17A30 | Nonassociative algebras satisfying other identities |
| 17A36 | Automorphisms, derivations, other operators (nonassociative rings and algebras) |
| 17B05 | Structure theory for Lie algebras and superalgebras |
| 17B40 | Automorphisms, derivations, other operators for Lie algebras and super algebras |
| 17C70 | Super structures |
References:
| [1] | DOI: 10.1080/00927872.2013.783040 · Zbl 1330.17007 · doi:10.1080/00927872.2013.783040 |
| [2] | DOI: 10.1006/jabr.2000.8617 · Zbl 1006.17024 · doi:10.1006/jabr.2000.8617 |
| [3] | DOI: 10.1016/j.jpaa.2003.10.005 · Zbl 1036.17006 · doi:10.1016/j.jpaa.2003.10.005 |
| [4] | DOI: 10.1006/jabr.1997.7144 · Zbl 0892.17005 · doi:10.1006/jabr.1997.7144 |
| [5] | DOI: 10.1016/0021-8693(87)90187-6 · Zbl 0605.16003 · doi:10.1016/0021-8693(87)90187-6 |
| [6] | Utumi Y., Osaka J. Math 8 pp 1– (1956) |
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