Invertible Preservers and Algebraic Groups II: Preservers of Similarity Invariants and Overgroups ofPSLn(F)

DOI10.1080/03081089708818527zbMath0889.20026OpenAlexW2083827772MaRDI QIDQ4376562

Robert M. Guralnick

Publication date: 10 March 1998

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

Full work available at URL: https://doi.org/10.1080/03081089708818527

zbMATH Keywords

algebraic groupsinvariant theorylinear preserversactionsexterior spacesovergroupsinvertible linear mapssubgroup structure of algebraic groups

Mathematics Subject Classification ID

Linear algebraic groups over arbitrary fields (20G15) Subgroup theorems; subgroup growth (20E07) Vector and tensor algebra, theory of invariants (15A72) Chains and lattices of subgroups, subnormal subgroups (20E15) Linear transformations, semilinear transformations (15A04)

Related Items

Multiplicative Preservers of C-Numerical Ranges and Radii, Linear preservers and representations with a 1-dimensional ring of invariants, On isometry groups of self-adjoint traceless and skew-symmetric matrices, Linear maps preserving orbits, Induced operators on symmetry classes of tensors, Overgroups of $E(m,R)⊗E(n,R)$ I. Levels and normalizers, Some general techniques on linear preserver problems, Trace form preservers

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Overgroups in GL(U\(\otimes W)\) of certain subgroups of GL(U)\(\otimes GL(W)\). I
• Linear preserver problems: A brief introduction and some special techniques
• Linear maps on matrices: the invariance of symmetric polynomials
• Trace form preservers
• Overgroups of some classical linear groups with applications to linear preserver problems
• Antidiagonals of matrices in a unitary similarity orbit
• Invertible preservers and algebraic groups
• On trace forms of higher degree
• Linear maps preserving commutativity
• Linear preserver problems and algebraic groups
• Invertibility of linear maps preserving matrix invariants
• On the Orders of Maximal Subgroups of the Finite Classical Groups
• The Affine Permutation Groups of Rank Three
• Inequalities for unitarily invariant norms and bilinear matrix products
• Invariants of linear maps on matrix algebras
• Linear operators preserving certain singular matrix sets
• Linear maps that preserve the commutant, double commutant or the lattice of invariant subspaces
• Factorizations of simple algebraic groups
• Subgroups of 𝐺𝐿(𝑛²,𝐂) containing 𝐏𝐒𝐔(𝐧)