Constants of Weitzenböck derivations and invariants of unipotent transformations acting on relatively free algebras.

DOI10.1016/j.jalgebra.2005.07.004zbMath1087.16023arXivmath/0412399OpenAlexW2085163933MaRDI QIDQ2572061

Vesselin Drensky, Chander Kanta Gupta

Publication date: 14 November 2005

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0412399

zbMATH Keywords

polynomial algebrasautomorphismsalgebras of invariantsvarieties of algebrasfinitely generated algebrasWeitzenböck derivationsrelatively free algebrasgeneric matricesrelatively free Lie algebraslinear derivationsalgebras of constants

Mathematics Subject Classification ID

Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.) (16S10) Actions of groups and semigroups; invariant theory (associative rings and algebras) (16W22) Identities, free Lie (super)algebras (17B01) Trace rings and invariant theory (associative rings and algebras) (16R30) Derivations, actions of Lie algebras (16W25)

Related Items (12)

Graded algebras, algebraic functions, planar trees, and elliptic integrals ⋮ A complete minimal system of covariants for the binary form of degree 7 ⋮ On Nowicki's conjecture: a survey and a new result ⋮ Rationality of Hilbert series in noncommutative invariant theory ⋮ Weitzenböck derivations of free metabelian Lie algebras ⋮ Coordinates and automorphisms of polynomial and free associative algebras of rank three. ⋮ Weitzenböck derivations of free metabelian associative algebras ⋮ The Nowicki conjecture for free metabelian Lie algebras ⋮ Another proof of the Nowicki conjecture ⋮ Classical invariant theory for free metabelian Lie algebras ⋮ Locally nilpotent derivations of free algebra of rank two ⋮ The Nowicki conjecture for relatively free algebras

Cites Work

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• Stably tame automorphisms
• Noncommutative invariants of finite groups and Noetherian varieties
• Codimensions of T-ideals and Hilbert series of relatively free algebras
• Constants of formal derivatives of non-associative algebras, Taylor expansions and applications
• Homogeneous polynomial identities
• Noncommutative invariants of reductive groups
• Hilbert series of fixed free algebras and noncommutative classical invariant theory
• On Engel-Lie algebras
• Algebras of invariants of free algebras
• Young diagrams and determinantal varieties
• Invariants mostly old ones
• The Poincaré series of the ring of 2x2 generic matrices
• Some formulas in invariant theory
• A basis of a free metabelian associative algebra
• The kernel of a derivation
• An algorithm to compute the invariant ring of a \(G_ a\)-action on an affine variety
• New automorphisms of generic matrix algebras and polynomial algebras
• Local slice constructions in \(k[X,Y,Z\)]
• Hopf co-addition for free magma algebras and the non-associative Hausdorff series.
• Multiplicities of Schur functions in invariants of two \(3\times 3\) matrices
• Über die Invarianten von linearen Gruppen
• Polynomial automorphisms and the Jacobian conjecture
• Finite basing of the identities of a matrix algebra of second order over a field of characteristic zero
• On the extension of automorphisms of polynomial rings
• A counterexample to Hilbert's fourteenth problem in dimension 5
• New stably tame automorphisms of polynomial algebras
• Generalization of the Hilbert theorem on the finiteness of bases
• On a theorem of Weitzenböck in invariant theory
• Gesetze in Ringen. I
• Konstanzelemente in Ringen mit Differentiation
• Actions of linearly reductive groups on affine PI algebras
• Invariant Bases for Free Lie Rings
• Weak polynomial identities for a vector space with a symmetric bilinear form
• Polynomial identities for a family of simple jordan algebras
• An algorithm for explicit generators of the invariants of the basic G_a—actions
• Trace rings of generic 2 by 2 matrices
• REPRESENTATIONS OF THE SYMMETRIC GROUP AND VARIETIES OF LINEAR ALGEBRAS
• Poincare series and a problem of S. Montgomery
• A Matrix Representation for Associative Algebras. I
• Finitely based ideals of weak polynomial identities
• A Hilbert-Nagata theorem in noncommutative invariant theory
• Exponential automorphisms of polynomial algebras
• On the rationality of Hilbert series of relatively free algebras
• An elementary proof of the Weitzenböck Theorem
• Fixed Algebras of Residually Nilpotent Lie Algebras
• Finite generation of invariants of finite linear groups on relatively free algebras
• On the Fixed Points of a Finite Group Acting on a Free Lie Algebra
• The Polynomial Identities of the Grassman Algebra
• Taylor expansion of noncommutative power series with an application to the Hausdorff series
• ALGORITHMIC PROBLEMS IN VARIETIES
• The Nagata automorphism is wild
• On the 14-th Problem of Hilbert

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