Separating \(G_2\)-invariants of several octonions

DOI10.2140/ANT.2024.18.2157MaRDI QIDQ6622893

Artem Lopatin, Alexandr N. Zubkov

Publication date: 23 October 2024

Published in: Algebra \& Number Theory (Search for Journal in Brave)

zbMATH Keywords

positive characteristicseparating setmatrix invariantspolynomial invariantsexceptional groupsgenerating set

Mathematics Subject Classification ID

Representation theory for linear algebraic groups (20G05) Group actions on varieties or schemes (quotients) (14L30) Actions of groups on commutative rings; invariant theory (13A50) Representations of groups as automorphism groups of algebraic systems (20F29) Alternative rings (17D05) Composition algebras (17A75)

Cites Work

• Maximal subalgebras of octonions
• Invariants of \(\mathrm G_2\) and Spin(7) in positive characteristic
• Invariant theory of \(G_ 2\) and \(Spin_ 7\)
• Instability in invariant theory
• Separating invariants for \(2 \times 2\) matrices
• Rings of matrix invariants in positive characteristic
• On invariants of \(F_ 4\) and the center of the Albert algebra
• Maximal subalgebras of the octonions
• Algorithms for orbit closure separation for invariants and semi-invariants of matrices
• Characteristic free description of semi-invariants of \(2 \times 2\) matrices
• The sextonions and \(E_{7\frac12}\)
• Separating invariants for arbitrary linear actions of the additive group
• Separating invariants over finite fields
• Separating invariants for the Klein four group and cyclic groups
• CLASSIFICATION OF SUBALGEBRAS OF THE CAYLEY ALGEBRA OVER A FINITE FIELD
• Separating invariants for multisymmetric polynomials
• Degree bound for separating invariants of abelian groups
• On maximal subalgebras

Related Items (1)

On \(m\)-tuples of nilpotent \(2\times 2\) matrices over an arbitrary field

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