By Skowronski A. (ed.)

This publication is anxious with contemporary traits within the illustration thought of algebras and its interesting interplay with geometry, topology, commutative algebra, Lie algebras, quantum teams, homological algebra, invariant concept, combinatorics, version idea and theoretical physics. the gathering of articles, written via prime researchers within the box, is conceived as a type of guide offering quick access to the current nation of data and stimulating extra improvement. the themes less than dialogue contain diagram algebras, Brauer algebras, mobile algebras, quasi-hereditary algebras, corridor algebras, Hecke algebras, symplectic mirrored image algebras, Cherednik algebras, Kashiwara crystals, Fock areas, preprojective algebras, cluster algebras, rank types, types of algebras and modules, moduli of representations of quivers, semi-invariants of quivers, Cohen-Macaulay modules, singularities, coherent sheaves, derived different types, spectral illustration thought, Coxeter polynomials, Auslander-Reiten conception, Calabi-Yau triangulated different types, Poincare duality areas, selfinjective algebras, periodic algebras, good module different types, Hochschild cohomologies, deformations of algebras, Galois coverings of algebras, tilting conception, algebras of small homological dimensions, illustration different types of algebras, and version conception. This ebook includes fifteen self-contained expository survey articles and is addressed to researchers and graduate scholars in algebra in addition to a broader mathematical neighborhood. They comprise a great number of open difficulties and provides new views for examine within the box.