This text is intended for graduate students and research mathematicians interested in algebraic geometry, category theory and homological algebra.
Generalized Dyson Series, Generalized Feynman's Diagrams, the Feynman Integral, and Feynman's Operational Calculus
The Künneth Theorem and the Universal Coefficient Theorem for Equivariant K-theory and KK-theory
In particular, in the 1-colored case (C = {∗}), this map is O(0) ≅ O(0) ⊗ I θ X. We call these maps the 0-ary action. In practice, the 0-ary action provides the O-algebra X with units. For example, suppose O is the 1-colored operad ...
The prototypical example of an operad is called the endomorphism operad of an object A with EA(n) = Hom(A⊗n ,A). Here the elements are normally called n-ary operations, and the structure map γ comes from using the outputs ...
Tensor Products of Principal Series Representations: Reduction of Tensor Products of Principal Series: Representations of Complex Semisimple Lie Groups
This is the second part of a series of papers called "HAG", devoted to developing the foundations of homotopical algebraic geometry.
The maps from loop suspensions to loop spaces are investigated using group representations in this article.
This book, prefaced by Yuri I. Manin, gives a rigorous overview of some of the main advances in the theory of noncommutative motives. It is divided into three main parts.
Rings, Modules and Algebras