Now showing items 1-20 of 22

• #### Abstract Bivariant Cuntz Semigroups ﻿

[OWP-2017-04] (Mathematisches Forschungsinstitut Oberwolfach, 2017-02-13)
We show that abstract Cuntz semigroups form a closed symmetric monoidal category. Thus, given Cuntz semigroups $S$ and $T$, there is another Cuntz semigroup $((S,T))$ playing the role of morphisms from $S$ to $T$. Applied ...
• #### The algebra of differential operators for a Gegenbauer weight matrix ﻿

[OWP-2015-07] (Mathematisches Forschungsinstitut Oberwolfach, 2015-07-29)
In this work we study in detail the algebra of differential operators $\mathcal{D}(W)$ associated with a Gegenbauer matrix weight. We prove that two second order operators generate the algebra, indeed $\mathcal{D}(W)$ is ...
• #### Composition of Irreducible Morphisms in Coils ﻿

[OWP-2017-32] (Mathematisches Forschungsinstitut Oberwolfach, 2017-10-30)
We study the non-zero composition of n irreducible morphisms between modules lying in coils in relation with the powers of the radical of their module category.
• #### Composition of Irreducible Morphisms in Quasi-Tubes ﻿

[OWP-2015-03] (Mathematisches Forschungsinstitut Oberwolfach, 2015-04-09)
We study the composition of irreducible morphisms between indecomposable modules lying in quasi-tubes of the Auslander-Reiten quivers of artin algebras $A$ in relation with the powers of the radical of their module category ...
• #### Dominance and Transmissions in Supertropical Valuation Theory ﻿

[OWP-2011-07] (Mathematisches Forschungsinstitut Oberwolfach, 2011)
This paper is a sequel of [IKR1], where we defined supervaluations on a commutative ring $R$ and studied a dominance relation $\Phi >= v$ between supervaluations $\varphi$ and $\upsilon$ on $R$, aiming at an enrichment of ...
• #### Geometry of Free Loci and Factorization of Noncommutative Polynomials ﻿

[OWP-2017-23] (Mathematisches Forschungsinstitut Oberwolfach, 2017-10-02)
The free singularity locus of a noncommutative polynomial f is defined to be the sequence $Z_n(f)=\{X\in M_n^g : \det f(X)=0\}$ of hypersurfaces. The main theorem of this article shows that f is irreducible if and only if ...
• #### Homological properties of piecewise hereditary algebras ﻿

[OWP-2009-11] (Mathematisches Forschungsinstitut Oberwolfach, 2009-03-05)
Let $\Lambda$ be a finite dimensional algebra over an algebraically closed field $k$. We will investigate homological properties of piecewise hereditary algebras $\Lambda$. In particular we give lower and upper bounds of ...
• #### Monoid valuations and value ordered supervaluations ﻿

[OWP-2011-17] (Mathematisches Forschungsinstitut Oberwolfach, 2011)
We complement two papers on supertropical valuation theory ([IKR1], [IKR2]) by providing natural examples of m-valuations (= monoid valuations), after that of supervaluations and transmissions between them. The supervaluations ...
• #### New representations of matroids and generalizations ﻿

[OWP-2011-18] (Mathematisches Forschungsinstitut Oberwolfach, 2011)
We extend the notion of matroid representations by matrices over fields by considering new representations of matroids by matrices over finite semirings, more precisely over the boolean and the superboolean semirings. This ...
• #### On Selfinjective Artin Algebras Having Generalized Standard Quasitubes ﻿

[OWP-2010-18] (Mathematisches Forschungsinstitut Oberwolfach, 2010-03-18)
We give a complete description of the Morita equivalence classes of all connected selfinjective artin algebras for which the Auslander-Reiten quiver admits a family of quasitubes having common composition factors, closed ...
• #### On the Derived Category of Grassmannians in Arbitrary Characteristic ﻿

[OWP-2013-24] (Mathematisches Forschungsinstitut Oberwolfach, 2013-12-09)
In this paper we consider Grassmannians in arbitrary characteristic. Generalizing Kapranov's well-known characteristic-zero results we construct dual exceptional collections on them (which are however not strong) as well ...
• #### Plethysms, replicated Schur functions and series, with applications to vertex operators ﻿

[OWP-2010-12] (Mathematisches Forschungsinstitut Oberwolfach, 2010-03-14)
Specializations of Schur functions are exploited to define and evaluate the Schur functions $s_\lambda [\alpha X]$ and plethysms $s_\lambda [\alpha s_\nu(X))]$ for any $\alpha$-integer, real or complex. Plethysms are then ...
• #### A series of algebras generalizing the Octonions and Hurwitz-Radon Identity ﻿

[OWP-2010-10] (Mathematisches Forschungsinstitut Oberwolfach, 2010)
We study non-associative twisted group algebras over $(\mathbb{Z}_2)^n$ with cubic twisting functions. We construct a series of algebras that extend the classical algebra of octonions in the same way as the Clifford algebras ...
• #### Simple vector bundles on plane degenerations of an elliptic curve ﻿

[OWP-2009-20] (Mathematisches Forschungsinstitut Oberwolfach, 2009-03-13)
In 1957 Atiyah classified simple and indecomposable vector bundles on an elliptic curve. In this article we generalize his classification by describing the simple vector bundles on all reduced plane cubic curves. Our main ...
• #### Supertropical linear algebra ﻿

[OWP-2010-14] (Mathematisches Forschungsinstitut Oberwolfach, 2010)
The objective of this paper is to lay out the algebraic theory of supertropical vector spaces and linear algebra, utilizing the key antisymmetric relation of "ghost surpasses." Special attention is paid to the various ...
• #### Supertropical Matrix Algebra III : Powers of Matrices and Generalized Eigenspaces ﻿

[OWP-2010-20] (Mathematisches Forschungsinstitut Oberwolfach, 2010)
We investigate powers of supertropical matrices, with special attention to the role of the coefficients of the supertropical characteristic polynomial (especially the supertropical trace) in controlling the rank of a power ...
• #### Supertropical Quadratic Forms I ﻿

[OWP-2013-27] (Mathematisches Forschungsinstitut Oberwolfach, 2013)
We initiate the theory of a quadratic form q over a semiring $R$. As customary, one can write $q(x+y)=q(x)+q(y)+b(x,y)$, where b is a companion bilinear form. But in contrast to the ring-theoretic case, the companion ...
• #### Supertropical semirings and supervaluations ﻿

[OWP-2010-05] (Mathematisches Forschungsinstitut Oberwolfach, 2010)
We interpret a valuation $\upsilon$ on a ring $R$ as a map $\upsilon:R \rightarrow M$ into a so called bipotent semiring $M$ (the usual max-plus setting), and then define a supervaluation $\varphi$ as a suitable map into ...
• #### Tensor Representations of q(∞) ﻿

[OWP-2016-09] (Mathematisches Forschungsinstitut Oberwolfach, 2016-06-17)
We introduce a symmetric monoidal category of modules over the direct limit queer superalgebra $\mathfrak{q}(\infty)$. The category can be defined in two equivalent ways with the aid of the large annihilator condition. ...
• #### Tilting on non-commutative rational projective curves ﻿

[OWP-2009-14] (Mathematisches Forschungsinstitut Oberwolfach, 2009-03-08)
In this article we introduce a new class of non-commutative projective curves and show that in certain cases the derived category of coherent sheaves on them has a tilting complex. In particular, we prove that the right ...