Related papers: Derived Algebraic Geometry
A general framework for obtaining certain types of contracted and centrally extended algebras is presented. The whole process relies on the existence of quadratic algebras, which appear in the context of boundary integrable models.
These are expanded notes from lectures given at the \'{E}tats de la Recherche workshop on "Derived algebraic geometry and interactions". These notes serve as an introduction to the emerging theory of Poisson structures on derived stacks.
Hopf algebra structure on the differential algebra of the extended $q$-plane is defined. An algebra of forms which is obtained from the generators of the extended $q$-plane is introduced and its Hopf algebra structure is given.
Generalised contact structures are studied from the point of view of reduced generalised complex structures, naturally incorporating non-coorientable structures as non-trivial fibering. The infinitesimal symmetries are described in detail,…
A perturbative formulation of algebraic field theory is presented, both for the classical and for the quantum case, and it is shown that the relation between them may be understood in terms of deformation quantization.
These are some notes on the basic properties of algebraic K-theory and G-theory of derived algebraic spaces and stacks, and the theory of fundamental classes in this setting.
Let $\mathfrak{g}$ be a Color Lie Algebra and $\mathcal{U}(\mathfrak{g})$ its the universal Enveloping Algebra. We define the notion of graded deformations and we give explicit graded deformations of the universal Enveloping Algebra of…
Phylogenetic algebraic geometry is concerned with certain complex projective algebraic varieties derived from finite trees. Real positive points on these varieties represent probabilistic models of evolution. For small trees, we recover…
One of the questions investigated in deformation theory is to determine to which algebras can a given associative algebra be deformed. In this paper we investigate a different but related question, namely: for a given associative…
This survey is an invitation to recent developments in higher dimensional birational geometry.
We discuss the homological algebra of representation theory of finite dimensional algebras and finite groups. We present various methods for the construction and the study of equivalences of derived categories: local group theory, geometry…
A general scheme for determining and studying integrable deformations of algebraic curves, based on the use of Lenard relations, is presented. We emphasize the use of several types of dynamical variables : branches, power sums and…
In this paper we investigate the possibility of constructing a complete quantization procedure consisting of geometric and deformation quantization. The latter assigns a noncommutative algebra to a symplectic manifold, by deforming the…
We develop the basic theory of derived quasi-coherent ideals for stacks relative to a given derived algebraic context. We compare different notions of adic completeness with respect to derived ideals, define and compare formal spectra and…
This paper describes a higher-categorical version of the theory of colored operads, giving applications to the study of commutative ring spectra.
It is a basic introduction to differential graded Lie algebras, Maurer-Cartan equation and associated deformation functors.
In this survey we discuss the results on the finitistic dimension of various stratified algebras. We describe what is already known, present some recent estimates, and list some open problems.
In this paper we investigate the problem of which Lie algebras appear as the derived algebra of a Lie algebra. We present new results that further develop this study and address two questions raised in a paper concerned with the…
This article surveys the development of the theory of algebraic geometry codes since their discovery in the late 70's. We summarize the major results on various problems such as: asymptotic parameters, improved estimates on the minimum…
A unified description of the relationship between the Hamiltonian structure of a large class of integrable hierarchies of equations and W-algebras is discussed. The main result is an explicit formula showing that the former can be…