This text is based on the notes for a series of five lectures to the Barcelona Summer School in Commutative Algebra at the Centre de Recerca Matematica, Institut d’Estudis Catalans, July 15–26, 1996

Infinite Free Resolutions

Algorithmic problems in varieties

We define a new monoidal category on collections (shuffle composition). Monoids in this category (shuffle operads) turn out to bring a new insight in the theory of symmetric operads. For this category, we develop the machinery of Grobner bases for operads, and present operadic versions of Bergman's Diamond Lemma and Buchberger's algorithm. This machinery can be applied to study symmetric operads. In particular, we obtain an effective algorithmic version of Hoffbeck's PBW criterion of Koszulness for (symmetric) quadratic operads.

Gr\"obner bases for operads

We review some known results and open problems related to the growth of groups. For a finitely generated group Γ, given whenever necessarytogether with a finite generating set, we discuss the notions of

/pdf/on-problems-related-to-growth-entropy-and-spectrum-in-group-3dbbf3pcci.pdf

On problems related to growth, entropy, and spectrum in group theory

Basic constructions. On nilpotency and colvability. Cartan subalgebras. Lie algebras with non-degenerate Killing form. The classification of the simple Lie algebras. Universal enveloping algebras. Finitely presented Lie algebras. Representations of semisimple Lie algebras. On associative algebras. Bibliography. Index of Symbols. Index of Terminology. Index of Algorithms.

Lie Algebras: Theory and Algorithms

http://link.springer.com/content/pdf/10.1007/978-3-662-06292-0_1.pdf

V. A. Ufnarovskij

Papers

Combinatorial and Asymptotic Methods in Algebra