Related papers: On the generalized SO(2n,C)-opers

Motivated by the geometry of certain hyperplane arrangements, Manin and Schechtman defined for each positive integer n a hierarchy of finite partially ordered sets B(n, k), indexed by positive integers k, called the higher Bruhat orders.…

The group of continuous binary operations on a topological space is studied; its relationship with the group of homeomorphisms is established. The category of binary $G$-spaces and bi-equivariant maps is constructed, which is a natural…

Rota-Baxter systems of T. Brzezi\'{n}ski are a generalization of Rota-Baxter operators that are related to dendriform structures, associative Yang-Baxter pairs and covariant bialgebras. In this paper, we consider Rota-Baxter systems in the…

On a smooth manifold M, generalized complex (generalized paracomplex) structures provide a notion of interpolation between complex (paracomplex) and symplectic structures on M. Given a complex manifold (M,j), we define six families of…

We argue that operads provide a general framework for dealing with polynomials and combinatory completeness of combinatory algebras, including the classical $\mathbf{SK}$-algebras, linear $\mathbf{BCI}$-algebras, planar…

The associative operad is a certain algebraic structure on the sequence of group algebras of the symmetric groups. The weak order is a partial order on the symmetric group. There is a natural linear basis of each symmetric group algebra,…

This survey paper is devoted to Riemannian manifolds with special holonomy. To any Riemannian manifold of dimension n is associated a closed subgroup of SO(n), the holonomy group; this is one of the most basic invariants of the metric. A…

The symplectic group branching algebra, B, is a graded algebra whose components encode the multiplicities of irreducible representations of Sp(2n-2,C) in each irreducible representation of Sp(2n,C). By describing on B an ASL structure, we…

We define the notions of B_n-generalized pseudo-Hermitian and B_n-generalized pseudo-Kahler structures on an odd exact Courant algebroid E. When E is in the standard form (or of type B_n) we express these notions in terms of classical…

In [M. R\"osler and M. Voit. Integral Representation and Uniform Limits for Some Heckman-Opdam Hypergeometric Functions of type BC, Transactions of the American Mathematical Society, Vol. 368, No. 8, 6005-6032, 2016.], R\"osler and Voit…

We generalize complex manifolds to manifolds with corners $X$, and to manifolds with generalized corners (g-corners) in the sense of the second author arXiv:1501.00401, using complex structures on the b-tangent bundle (log tangent bundle)…

Operator systems connect operator algebra, free semialgebraic geometry and quantum information theory. In this work we generalize operator systems and many of their theorems. While positive semidefinite matrices form the underlying…

We introduce simple models for associative algebras and bimodules in the context of non-symmetric $\infty$-operads, and use these to construct an $(\infty,2)$-category of associative algebras, bimodules, and bimodule homomorphisms in a…

We relate the Weyr structure of a square matrix $B$ to that of the $t \times t$ block upper triangular matrix $C$ that has $B$ down the main diagonal and first superdiagonal, and zeros elsewhere. Of special interest is the case $t = 2$ and…

In math.SG/0605587, we studied Yang-Mills functional on the space of connections on a principal G_R-bundle over a closed, connected, nonorientable surface, where G_R is any compact connected Lie group. In this sequel, we generalize the…

In the classical operator theory, there are several versions of spectra, related to special classes of operators (Fredholm, semi-Fredholm, upper/lower semi-Fredholm,etc.). We generalize these notions for adjointable operators on Hilbert…

Quadratic algebras are generalizations of Lie algebras which include the symmetry algebras of 2nd order superintegrable systems in 2 dimensions as special cases. The superintegrable systems are exactly solvable physical systems in classical…

An $\mathcal{O}$-operator has been used to extend a Leibniz algebra by its representation. In this paper, we investigate several structures related to $\mathcal{O}$-operators on Leibniz algebras and introduce (dual)…

We introduce the concept of G2(2)-structure on an orientable 3-manifold M using the setting of generalized geometry of type Bn, study their local deformation by making use of a Moser-type argument, and give a description of the cone of…

Let H be a complex Hilbert space and denote by Bs(H) the set of all self-adjoint bounded linear operators on H. In this paper we describe the form of all bijective maps (no linearity or continuity is assumed) on Bs(H) which preserve the…