Related papers: Frobenius nilHecke algebras
The notion of a Frobenius manifold appears in relation to various topics in algebraic and analytic geometry, such and quantum cohomology, deformation of meromorphic connections, unfolding of singularities and others. In the local setting…
Two rings A and B are said to be derived Morita equivalent if their derived categories of modules are equivalent. By results of Rickard, if A and B are derived Morita equivalent algebras over a field k, then there is a complex of bimodules…
We develop the theory of linear algebra over a (Z_2)^n-commutative algebra (n in N), which includes the well-known super linear algebra as a special case (n=1). Examples of such graded-commutative algebras are the Clifford algebras, in…
We formulate a type B extended nilHecke algebra, following the type A construction of Naisse and Vaz. We describe an action of this algebra on extended polynomials and describe some results on the structure on the extended symmetric…
We construct a class of infinite-dimensional Frobenius manifolds on the space of pairs of certain even functions meromorphic inside or outside the unit circle. Via a bi-Hamiltonian recursion relation, the principal hierarchies associated to…
We consider algebraic varieties canonically associated to any Lie superalgebra, and study them in detail for super-Poincar\'e algebras of physical interest. They are the locus of nilpotent elements in (the projectivized parity reversal of)…
Given the algebra, Hilbert space H, grading and real structure of the finite spectral triple of the Standard Model, we classify all possible Dirac operators such that H is a self-Morita equivalence bimodule for the associated Clifford…
Commutative Hilbertian Frobenius algebras are those commutative semi-group objects in the monoidal category of Hilbert spaces, for which the Hilbert adjoint of the multiplication satisfies the Frobenius compatibility relation, that is, this…
We define the notions of unital/counital/biunital infinitesimal anti-symmetric bialgebras and coFrobenius bialgebras and discuss their algebraic properties. We also define the notion of a graded 2D open-closed TQFT. These structures arise…
The notion of a Z-algebra has a non-linear analogue, whose purpose it is to control operations on commutative rings rather than linear operations on abelian groups. These plethories can also be considered non-linear generalizations of…
In this paper we discuss some connections between groupoids and Frobenius algebras specialized in the case of Poisson sigma models with boundary. We prove a correspondence between groupoids in the category Set and relative Frobenius…
Among its many corollaries, Poincare duality implies that the de Rham cohomology of a compact oriented manifold is a shifted commutative Frobenius algebra --- a commutative Frobenius algebra in which the comultiplication has cohomological…
Let $U$ be the quantum group with divided powers in $l-$th root of unity and let $u\subset U$ be the Frobenius kernel. V.Ginzburg and S.Kumar proved that the cohomology algebra of $u$ with trivial coefficients is isomorphic to the functions…
We use the differential algebra of polytopes to explain the known remarkable relation of the combinatorics of the associahedra and permutohedra with the universal compositional and multiplicative inversion formulas for the formal power…
We provide general closed-form formulas for the index of type-A Lie poset algebras corresponding to posets of restricted height. Furthermore, we provide a combinatorial recipe for constructing all posets corresponding to type-A Frobenius…
We classify all nonnilpotent, solvable Leibniz algebras with the property that all proper subalgebras are nilpotent. This generalizes the work of Stitzinger and Towers in Lie algebras. We show several examples which illustrate the…
We introduce the notion of a quasi-Frobenius algebra in a finite tensor category $\mathcal{C}$ and give equivalent conditions for an algebra in $\mathcal{C}$ to be quasi-Frobenius. A quasi-Frobenius algebra in $\mathcal{C}$ is not…
Leibniz algebras are certain generalization of Lie algebras. In this paper we give the classification of four dimensional non-Lie nilpotent Leibniz algebras. We use the canonical forms for the congruence classes of matrices of bilinear…
The description of complex solvable Leibniz algebras whose nilradical is a naturally graded filiform algebra is already known. Unfortunately, a mistake was made in that description. Namely, in the case where the dimension of the solvable…
Let $\ell, n$ be positive integers such that $\ell\geq n$. Let $\mathbb{G}_{n,\ell}$ be the Grassmannian which consists of the set of $n$-dimensional subspaces of $\mathbb{C}^{\ell}$. There is a $\mathbb{Z}$-graded algebra isomorphism…