Growth in enveloping algebras

DOI10.1007/BF02760603zbMath0552.17006MaRDI QIDQ801017

A. I. Lichtman

Publication date: 1984

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

zbMATH Keywords

universal enveloping algebragrowth functionsubexponential growthinfinite dimensional algebraOre domainsolvable-by-finite Lie algebraWreath products

Mathematics Subject Classification ID

Universal enveloping (super)algebras (17B35) Infinite-dimensional Lie (super)algebras (17B65) Solvable, nilpotent (super)algebras (17B30) Chain conditions on annihilators and summands: Goldie-type conditions (16P60) Integral domains (associative rings and algebras) (16U10)

Related Items (12)

Graded algebras, algebraic functions, planar trees, and elliptic integrals ⋮ The residual nilpotence of the multiplicative group of a skew field generated by universal enveloping algebras ⋮ Clover nil restricted Lie algebras of quasi-linear growth ⋮ PI-subrings and algebraic elements in enveloping algebras and their fields of fractions ⋮ Schreier's type formulae and two scales for growth of Lie algebras and groups ⋮ Nil restricted Lie algebras of oscillating intermediate growth ⋮ Lie algebras with finite Gelfand-Kirillov dimension ⋮ GROWTH OF FINITELY GENERATED POLYNILPOTENT LIE ALGEBRAS AND GROUPS, GENERALIZED PARTITIONS, AND FUNCTIONS ANALYTIC IN THE UNIT CIRCLE ⋮ POLYCYCLIC RESTRICTED LIE ALGEBRAS ⋮ GROWTH OF SOLVABLE LIE SUPERALGEBRAS ⋮ Intermediate growth in finitely presented algebras ⋮ Intermediate growth of solvable Lie superalgebras

Cites Work

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• On matrix rings and linear groups over fields of fractions of group rings and enveloping algebras. II
• Über die Gelfand-Kirillov-Dimension. (On the Gelfand-Kirillov-dimension)
• A note on curvature and fundamental group
• Growth of finitely generated solvable groups and curvature of Riemannian manifolds
• Universal Enveloping Algebras with Subexponential but not Polynomially Bounded Growth

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