The Lascoux, Leclerc and Thibon algorithm and Soergel's tilting algorithm

We generalize Soergel's tilting algorithm to singular weights and deduce from this the validity of the Lascoux-Leclerc-Thibon conjecture on the connection between the canonical basis of the basic submodule of the Fock module and the representation theory of the Hecke-algebras at root of unity. Supported in part by Programa Reticulados y Ecuaciones and by FONDECYT grant 1051024.     

On deformed preprojective algebras

Deformed preprojective algebras are generalizations of the usual preprojective algebras introduced by Crawley-Boevey and Holland, which have applications to Kleinian singularities, the Deligne-Simpson problem, integrable systems and noncommutative geometry. In this paper we offer three contributions to the study of such algebras: (1) the 2-Calabi-Yau property; (2) the unification of the reflection functors of Crawley-Boevey and Holland with reflection functors for the usual preprojective algebras; and (3) the classification of tilting ideals in 2-Calabi-Yau algebras, and especially in deformed preprojective algebras for extended Dynkin quivers.     

Evolutive and nonlinear vibrations of rotor on aerodynamic bearings

The use of air as a lubricant in aerodynamic bearings is advantageous, particularly in the food industry. Aerodynamic bearings with tilting pads have complicated stiffness and damping properties and need a very detailed theoretical and experimental research. Response curves of rigid rotor supported on aerodynamic bearings are presented for a linear but evolutive mathematical model. Due to non-monotone properties of stiffness and damping matrices at variable revolutions, a new resonance appears. The mathematical model of rotor vibrations in the whole area of bearing clearance is also developed in the consideration of strongly nonlinear properties of aerodynamic bearing.     

Lifting to Cluster-Tilting Objects in 2-Calabi–Yau Triangulated Categories

We show that a tilting module over the endomorphism algebra of a cluster-tilting object in a 2-Calabi–Yau triangulated category lifts to a cluster-tilting object in this 2-Calabi–Yau triangulated category. This generalizes a recent work of Smith for cluster categories.     

Self-Orthogonal Modules of Finite Projective Dimension

Let R be a ring and _R ω a self-orthogonal module. We introduce the notion of the right orthogonal dimension (relative to _R ω) of modules. We give a criterion for computing this relative right orthogonal dimension of modules. For a left coherent and semilocal ring R and a finitely presented self-orthogonal module _R ω, we show that the projective dimension of _R ω and the right orthogonal dimension (relative to _R ω) of R/J are identical, where J is the Jacobson radical of R. As a consequence, we get that _R ω has finite projective dimension if and only if every left (finitely presented) R-module has finite right orthogonal dimension (relative to _R ω). If ω is a tilting module, we then prove that a left R-module has finite right orthogonal dimension (relative to _R ω) if and only if it has a special ω^⊥-preenvelope.     

Homogeneous Deformations of Brauer Tree Algebras

Abstract

Based on tilting theory, we demonstrate the existence of homogeneous deformations for the Brauer tree algebras, which are derived naturally from a tilting complex.     

Complements to Projective Almost Complete Tilting Modules

ABSTRACT

An equivalent version of the Generalized Nakayama Conjecture states that any projective almost complete tilting module admits a finite number of non-isomorphic indecomposable complements. Motivated by this connection, we investigate the number of possible complements of projective almost complete tilting modules for some particular classes of Artin algebras, namely monomial algebras and algebras with exactly two simple modules.