Polynomial identities for 2\(\times 2\) matrices

DOI10.1007/BF00053295zbMath0717.16021OpenAlexW4242716100MaRDI QIDQ753911

Vesselin Drensky

Publication date: 1990

Published in: Acta Applicandae Mathematicae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00053295

zbMATH Keywords

surveygeneral linear groupssymmetric groupsmatrix algebrarepresentationsHilbert seriesvarietypolynomial identitiescodimensionsPI-algebrasrelatively free algebrascocharactersminimal basisT-ideal

Mathematics Subject Classification ID

Representations of finite symmetric groups (20C30) Trace rings and invariant theory (associative rings and algebras) (16R30) (T)-ideals, identities, varieties of associative rings and algebras (16R10) Semiprime p.i. rings, rings embeddable in matrices over commutative rings (16R20) Research exposition (monographs, survey articles) pertaining to associative rings and algebras (16-02)

Related Items (6)

Growth for algebras satisfying polynomial identities. ⋮ Identities of representations of nilpotent lie algebras ⋮ Relatively free invariant algebras of finite reflection groups ⋮ Generic \(2\times 2\) matrices in positive characteristic ⋮ Finite generation of invariants of finite linear groups on relatively free algebras ⋮ New polynomial identities for \(2\times 2\) generic matrices in characteristic \(2\)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Computing with 2\(\times 2\) matrices
• Invariants and the ring of generic matrices
• Codimensions of T-ideals and Hilbert series of relatively free algebras
• Homogeneous polynomial identities
• Explicit codimension formulas of certain T-ideals
• The Poincaré series of the ring of 2x2 generic matrices
• The invariant theory of \(n\times n\) matrices
• Polynomial identities of nonassociative rings. III: Applications
• Existence of identities in \(A \otimes B\)
• Gesetze in Ringen. I
• Trace rings of generic 2 by 2 matrices
• REPRESENTATIONS OF THE SYMMETRIC GROUP AND VARIETIES OF LINEAR ALGEBRAS
• The polynomial identities of matrices
• On Symmetrized Kronecker Powers and the Structure of the Free Lie Ring

This page was built for publication: Polynomial identities for 2\(\times 2\) matrices