A generalization of Cayley-Hamilton algebras and an introduction to their geometries

DOI10.1007/S11856-024-2614-0MaRDI QIDQ6635459

Charles Almeida, José Lucas Galdino, Claudemir Fidelis

Publication date: 12 November 2024

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

Mathematics Subject Classification ID

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)

Cites Work

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• Kemer's theorem for affine PI algebras over a field of characteristic zero.
• Classification of group gradings on simple Lie algebras of types \(\mathcal A\), \(\mathcal B\), \(\mathcal C\) and \(\mathcal D\)
• Trace identities of the Jordan algebra of a bilinear form
• Invariants of \(\mathrm G_2\) and Spin(7) in positive characteristic
• A formal inverse to the Cayley-Hamilton theorem
• Invariant theory of \(G_ 2\) and \(Spin_ 7\)
• The invariant theory of \(n\times n\) matrices
• Laplace operator and polynomial invariants
• Supertraces and matrices over Grassmann algebras
• Embeddings for the Jordan algebra of a bilinear form
• Matrices with involution and invariant theory
• Polynomial identity rings.
• Examples and counterexamples for \(M_{1,1}\) embeddings
• Köthe's problem, Kurosh-Levitzky problem and graded rings
• An example in PI-rings
• On the immersion of an algebraic ring into a field
• Gradings on simple Lie algebras
• Embedding theoems for superalgebras
• Invariant theory of 𝐺₂
• Trace Identities and Z/2Z-Graded Invariants
• Identities of associative algebras
• Graded Brauer Groups.
• A Noncommutative Hilbert Basis Theorem and Subrings of Matrices
• The classical groups, their invariants and representations.

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