The entropy of graded algebras

DOI10.1006/jabr.1999.8053zbMath0963.16046OpenAlexW1991121321MaRDI QIDQ1969117

Csaba Schneider, M. F. Newman, Aner Shalev

Publication date: 28 August 2000

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jabr.1999.8053

zbMATH Keywords

entropygrowthpresentationsgraded algebrasfree productssymbolic dynamicsfree associative algebrasfree Lie algebrasHilbert seriesfree algebraslower central series

Mathematics Subject Classification ID

Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.) (16S10) Growth rate, Gelfand-Kirillov dimension (16P90) Identities, free Lie (super)algebras (17B01) Graded Lie (super)algebras (17B70) Free nonabelian groups (20E05) Graded rings and modules (associative rings and algebras) (16W50) Derived series, central series, and generalizations for groups (20F14) Free nonassociative algebras (17A50)

Related Items

Dimension and randomness in groups acting on rooted trees, Enumeration of algebras close to absolutely free algebras and binary trees, Growth of monomial algebras, simple rings and free subalgebras, Growth of subalgebras and subideals in free Lie algebras, Growth, entropy and commutativity of algebras satisfying prescribed relations., Graded algebras and their differential graded extensions., Pro‐p groups of positive rank gradient and Hausdorff dimension, On the verbal width of finitely generated pro-\(p\) groups., Asymptotically optimal \(k\)-step nilpotency of quadratic algebras and the Fibonacci numbers, Finite dimensional semigroup quadratic algebras with the minimal number of relations, Moderate deviations for the overlap parameter in the Hopfield model, Entropy of generating series for nonlinear input-output systems and their interconnections, Graded Lie algebras of type FP

Cites Work

• Homogeneous polynomial identities
• Non-commutative graded algebras and their Hilbert series
• Über die Gelfand-Kirillov-Dimension. (On the Gelfand-Kirillov-dimension)
• Free subalgebras of free associative algebras
• Universal Enveloping Algebras with Subexponential but not Polynomially Bounded Growth
• An Introduction to Symbolic Dynamics and Coding
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