Deformations of Lie brackets: cohomological aspects
We introduce a new cohomology for Lie algebroids, and prove that it provides a differential graded Lie algebra which “controls” deformations of the structure bracket of the algebroid.
Deformed commutators on comodule algebras over coquasitriangular Hopf algebras
We construct quantum commutators on comodule algebras over coquasitriangular Hopf algebras, so that they are quantum group coinvariant and have the generalized antisymmetry and Leibniz properties. If the coquasitriangular Hopf algebra is additionally cotriangular, then the quantum commutators satisfy a generalized Jacobi identity, and turn the comodule algebra into a quantum Lie algebra. Moreover, we investigate the projective and injective dimensions of some Doi-Hopf modules over a quantum commutative...
Deformed enveloping algebras.
Deformed mesh algebras of Dynkin type ℂₙ
In our recent paper (J. Algebra 345 (2011)) we prove that the deformed preprojective algebras of generalized Dynkin type ₙ (in the sense of our earlier work in Trans. Amer Math. Soc. 359 (2007)) are exactly (up to isomorphism) the stable Auslander algebras of simple plane singularities of Dynkin type . In this article we complete the picture by showing that the deformed mesh algebras of Dynkin type ℂₙ are isomorphic to the canonical mesh algebras of type ℂₙ, and hence to the stable Auslander algebras...
Degenerations for indecomposable modules and tame algebras
Degenerations for modules over representation-finite selfinjective algebras
Degenerations for representations of quivers with relations
Degenerations for representations of tame quivers
Degenerations in the module varieties of almost cyclic coherent Auslander-Reiten components
We establish when the partial orders and coincide for all modules of the same dimension from the additive category of a generalized standard almost cyclic coherent component of the Auslander-Reiten quiver of a finite-dimensional algebra.
Degenerations in the Module Varieties of Generalized Standard Auslander-Reiten Components
Degree 1 and 2 representations of nilpotent groups and applications to units of group rings.
Degree estimate for subalgebras generated by two elements
We develop a new combinatorial method to deal with a degree estimate for subalgebras generated by two elements in different environments. We obtain a lower bound for the degree of the elements in two-generated subalgebras of a free associative algebra over a field of zero characteristic. We also reproduce a somewhat refined degree estimate of Shestakov and Umirbaev for the polynomial algebra, which plays an essential role in the recent celebrated solution of the Nagata conjecture and the strong...
Dependent elements of derivations on semiprime rings.
Der Wedderburnsche Hauptsatz für alternative Tripelsysteme und Paare.
Derivation-like mappings for normal elements in prime rings with involution.
Derivations and multilinear polynomials
Derivations in rings with involution
Derivations in some finite endomorphism semirings
The goal of this paper is to provide some basic structure information on derivations in finite semirings.
Derivations of higher order in semiprime rings.
Derivations of Skew Polynomial Rings