Their topics include normal forms for vectors and univariate polynomials, twisted associative algebras and shuffle algebras, operadic homological algebra
and Gr|bner bases, linear algebra over polynomial rings, and a case study of non-symmetric ternary quadratic operads.
The subject area is an innovative blend of group theory, homological algebra
, topology, geometry, number theory and computer science.
Some notions of homological algebra
should be recalled from [3, 13], in order to formulate the next result.
He assumes students are familiar with homological algebra
, algebraic topology based on different forms, and de Rham cohomology.
We present here a synopsis of the results together with applications of this beautiful interplay between combinatorial topology and homological algebra
Universal q-differential calculus and q-analog of homological algebra
This two-volume research monograph on the general Lagrangian Floer theory and the accompanying homological algebra
of filtered $A_\infty$-algebras provides the most important step towards a rigorous foundation of the Fukaya category in general context.
Davis, A vanishing theorem in homological algebra
For example, set theory was invented in order to help in analysing the convergence behaviour of Fourier series; homological algebra
was invented in order to serve algebraic topology, and category theory was first developed with the view of applying it in homological algebra
(as well as algebraic topology and algebraic geometry).
Lubkin introduces entirely new invariants in homological algebra
and commutative and even non-commutative algebra that have never been considered before.
Positselski, Homological algebra
of semimodules and semicontramodules.
Some familiarity with basic homological algebra
is needed in the final chapter.