Salemkar, Ali Reza; Alamian, Vahid; Mohammadzadeh, Hamid Some properties of the Schur multiplier and covers of Lie algebras. (English) Zbl 1132.17003 Commun. Algebra 36, No. 2, 697-707 (2008). Summary: We give the structure of all covers of Lie algebras that their Schur multipliers are finite dimensional, which generalizes the work of P. Batten and E. Stitzinger [Commun. Algebra 24, No. 14, 4301–4317 (1996; Zbl 0893.17004)]. Also, similar to a result of K. Yamazaki [J. Fac. Sci., Univ. Tokyo, Sect. I 10, 147–195 (1964; Zbl 0125.01601)] in the group case, it is shown that each stem extension of a finite dimensional Lie algebra is a homomorphic image of a stem cover for it. Moreover, we introduce an ideal in every Lie algebra, which is the smallest ideal contained in the center whose factor algebra is capable, and give some different forms of this ideal. Finally, we study the connection between this ideal and the concept of the Schur multiplier. Cited in 1 ReviewCited in 56 Documents MSC: 17B30 Solvable, nilpotent (super)algebras 17B60 Lie (super)algebras associated with other structures (associative, Jordan, etc.) 17B99 Lie algebras and Lie superalgebras Keywords:isoclinism; Lie algebra; Schur multiplier Citations:Zbl 0125.01601; Zbl 0893.17004 PDFBibTeX XMLCite \textit{A. R. Salemkar} et al., Commun. Algebra 36, No. 2, 697--707 (2008; Zbl 1132.17003) Full Text: DOI References: [1] Batten , P. ( 1993 ). Covers and Multipliers of Lie Algebras . Ph.D. dissertation , North Carolina State University . [2] Batten P., Comm. Alg. 24 pp 4301– (1996) · Zbl 0893.17004 · doi:10.1080/00927879608825816 [3] Batten P., Comm. Alg. 24 pp 4319– (1996) · Zbl 0893.17008 · doi:10.1080/00927879608825817 [4] Hall P., J. Reine Angew. Math. 182 pp 130– (1940) [5] Hardy P., Comm. Alg. 33 pp 4205– (2005) · Zbl 1099.17007 · doi:10.1080/00927870500261512 [6] Jones M. R., Bull. Austral. Math. Soc. 11 pp 71– (1974) · Zbl 0282.20019 · doi:10.1017/S0004972700043653 [7] Karpilovsky G., London Math. Soc. Monographs New Series 2 (1987) [8] Moneyhun K., Algebra, Groups and Geometries 11 pp 9– (1994) [9] Schur I., J. Reine Angew. Math. 127 pp 20– (1904) [10] Yamazaki K., J. Fac. Sci. Univ. Tokyo, Sect I 10 pp 147– (1964) [11] Yankosky B., J. Lie Theor. 13 pp 1– (2003) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.