Related papers: Differential Homological Algebra and General Relat…

Homogeneous spaces are de Branges' Hilbert spaces of entire functions with the property that certain weighted rescaling transforms induce isometries of the space into itself. A classical example of a homogeneous space is the Paley-Wiener…

Let R and S be differential graded algebras. In this paper we give a characterisation of when a differential graded R-S-bimodule M induces a full embedding of derived categories M\otimes - :D(S)--> D(R). In particular, this characterisation…

Koszul property was generalized to homogeneous algebras of degree N>2 in [5], and related to N-complexes in [7]. We show that if the N-homogeneous algebra A is generalized Koszul, AS-Gorenstein and of finite global dimension, then one can…

In his famous paper [2], Demazure introduced certain indecomposable modules and used them to give a short proof of Bott's theorem. In this paper we consider a generalization of these modules and give their cohomology.

We give detailed exposition of modern differential geometry from global coordinate independent point of view as well as local coordinate description suited for actual computations. In introduction, we consider Euclidean spaces and different…

Motivated by previous work leveraging factorizations of second- and fourth-order differential operators, a general integral inequality involving higher order derivatives is proven by elementary means. It is then shown how this framework…

In this paper, we study the Fenchel-Rockafellar duality and the Lagrange duality in the general frame work of vector spaces without topological structures. We utilize the geometric approach, inspired from its successful application by B. S.…

We give an algebraic construction of standard modules (infinite dimensional modules categorifying the PBW basis of the underlying quantized enveloping algebra) for Khovanov-Lauda-Rouquier algebras in all finite types. This allows us to…

A differential algebra of finite type over a field k is a filtered algebra A, such that the associated graded algebra is finite over its center, and the center is a finitely generated k-algebra. The prototypical example is the algebra of…

Support varieties for any finite dimensional algebra over a field were introduced by Snashall-Solberg using graded subalgebras of the Hochschild cohomology. We mainly study these varieties for selfinjective algebras under appropriate finite…

We provide new insight into a {\em generalized conditional subgradient} algorithm and a {\em generalized mirror descent} algorithm for the convex minimization problem \[ \min_x \; \{f(Ax) + h(x)\}.\] As Bach showed in [{\em SIAM J. Optim.},…

It is proved that the sum of the Loewy lengths of the homology modules of a finite free complex F over a local ring R is bounded below by a number depending only on R. This result uncovers, in the structure of modules of finite projective…

Gauge duality theory was originated by Freund [Math. Programming, 38(1):47-67, 1987] and was recently further investigated by Friedlander, Mac{\^e}do and Pong [SIAM J. Optm., 24(4):1999-2022, 2014]. When solving some matrix optimization…

The linearizability of differential equations was first considered by Lie for scalar second order semi-linear ordinary differential equations. Since then there has been considerable work done on the algebraic classification of linearizable…

Let $R$ be a commutative Noetherian local ring and let $\fa$ be a proper ideal of $R$. A non-zero finitely generated $R$-module $M$ is called relative Cohen-Macaulay with respect to $\fa$ if there is precisely one non vanishing local…

In this paper we obtain a 2+2 double null Hamiltonian description of General Relativity using only the (complex) SO(3) connection and the components of the complex densitised self-dual bivectors. We carry out the general canonical analysis…

Let R be a commutative Noetherian ring, a a proper ideal of R and M a finite R-module. It is shown that, if (R;m) is a complete local ring, then under certain conditions a contains a regular element on DR(Hc a(M)), where c = cd(a;M). A…

When ${\cal{D}}$ is a linear partial differential operator of any order, a direct problem is to look for an operator ${\cal{D}}_1$ generating the compatibility conditions (CC) ${\cal{D}}_1\eta=0$ of ${\cal{D}}\xi=\eta$. We may thus…

In 1953, the physicists E. Inon\"u and E.P. Wigner introduced the concept of deformation of a Lie algebra by claiming that the limit $1/c \rightarrow 0$, when c is the speed of light, of the composition law $(u,v) \rightarrow…

The notion of a duality between two derived functors as well as an extension theorem for derived functors to larger categories in which they need not be defined is introduced. These ideas are then applied to extend and study the coext…