Poincare series and a problem of S. Montgomery

DOI10.1080/03081088208817467zbMath0493.15020OpenAlexW2012273852MaRDI QIDQ3955521

Warren Dicks, Edward W. Formanek

Publication date: 1982

Published in: Linear and Multilinear Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03081088208817467

zbMATH Keywords

invariant theorysymmetric algebratensor algebrafinitely generatedPoincare seriesfree associative k-algebra

Mathematics Subject Classification ID

Vector and tensor algebra, theory of invariants (15A72)

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Invariants of a free linear category and representation type, Graded algebras, algebraic functions, planar trees, and elliptic integrals, Hilbert series of fixed free algebras and noncommutative classical invariant theory, Walks on graphs and their connections with tensor invariants and centralizer algebras, Noncommutative invariants of bialgebras, Finitely generated invariants of Hopf algebras on free associative algebras., A noncrossing basis for noncommutative invariants of \(SL(2, \mathbb C)\), Symmetric polynomials in free associative algebras, Symmetric polynomials in the free metabelian Lie algebras, Invariant theory of free bicommutative algebras, Words and polynomial invariants of finite groups in non-commutative variables, Prime ideals in fixed rings of free algebras, A new index for polytopes, Relatively free invariant algebras of finite reflection groups, Invariants of universal enveloping algebras of relatively free Lie algebras, Unnamed Item, Topological automorphism groups of compact quantum groups, Rationality of the Hilbert series of Hopf-invariants of free algebras, Fixed Algebras of Residually Nilpotent Lie Algebras, Noncommutative classical invariant theory, S-algebras and commutative rings, Noncommutative classical invariant theory, Finite generation of invariants of finite linear groups on relatively free algebras, Constants of Weitzenböck derivations and invariants of unipotent transformations acting on relatively free algebras., Symmetric polynomials of algebras related with 2 × 2 generic traceless matrices, Invariants of finite linear groups on relatively free algebras, Symmetric polynomials in the variety generated by Grassmann algebras, Noncommutative invariants of reductive groups, Invariants of finite cyclic groups acting on generic matrices, Symmetric polynomials in the free metabelian Poisson algebras

Cites Work

• The number of nonfree components in the decomposition of symmetric powers in characteristic p
• Algebras of invariants of free algebras
• Invariants of finite groups and their applications to combinatorics
• Hilbert's Fourteenth Problem