• Abstract Bivariant Cuntz Semigroups 

      [OWP-2017-04] Antoine, Ramon; Perera, Francesc; Thiel, Hannes (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] Ignacio Nahuel Zurrián (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 ...
    • Cataland: Why the Fuß? 

      [OWP-2019-01] Stump, Christian; Thomas, Hugh; Williams, Nathan (Mathematisches Forschungsinstitut Oberwolfach, 2019-01-21)
      The three main objects in noncrossing Catalan combinatorics associated to a finite Coxeter system are noncrossing partitions, clusters, and sortable elements. The first two of these have known Fuß-Catalan generalizations. ...
    • Composition of Irreducible Morphisms in Coils 

      [OWP-2017-32] Chaio, Claudia; Malicki, Piotr (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] Chaio, Claudia; Malicki, Piotr (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] Izhakian, Zur; Knebusch, Manfred; Rowen, Louis (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 ...
    • The First Hochschild Cohomology as a Lie Algebra 

      [OWP-2019-09] Rubio y Degrassi, Lleonard; Schroll, Sibylle; Solotar, Andrea (Mathematisches Forschungsinstitut Oberwolfach, 2019-04-16)
      In this paper we study sufficient conditions for the solvability of the first Hochschild cohomology of a finite dimensional algebra as a Lie algebra in terms of its Ext-quiver in arbitrary characteristic. In particular, ...
    • Geometry of Free Loci and Factorization of Noncommutative Polynomials 

      [OWP-2017-23] Helton, J. William; Klep, Igor; Volčič, Jurij; Helton, J. William (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 ...
    • Group-Graded Rings Satisfying the Strong Rank Condition 

      [OWP-2019-22] Kropholler, Peter H.; Lorensen, Karl (Mathematisches Forschungsinstitut Oberwolfach, 2019-08-16)
      A ring $R$ satisfies the $\textit{strong rank condition}$ (SRC) if, for every natural number $n$, the free $R$-submodules of $R^n$ all have rank $\leq n$. Let $G$ be a group and $R$ a ring strongly graded by $G$ such that ...
    • Homological properties of piecewise hereditary algebras 

      [OWP-2009-11] Happel, Dieter; Zacharia, Dan (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 ...
    • Maximal Quaternion Orders in Quadratic Extensions - in Hurwitz’s Diaries 

      [OWP-2020-16] Oswald, Nicola; Steuding, Jörn (Mathematisches Forschungsinstitut Oberwolfach, 2020-08-03)
      We present and comment on some unpublished work of Adolf Hurwitz on quaternion arithmetic from his diaries.
    • Monoid valuations and value ordered supervaluations 

      [OWP-2011-17] Izhakian, Zur; Knebusch, Manfred; Rowen, Louis (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] Izhakian, Zur; Rhodes, John L. (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] Karpicz, Maciej; Skowroński, Andrzej; Yamagata, Kunio (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] Buchweitz, Ragnar-Olaf; Leuschke, Graham J.; Van den Bergh, Michel (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 ...
    • On the Lie Algebra Structure of $HH^1(A)$ of a Finite-Dimensional Algebra A 

      [OWP-2019-10] Linckelmann, Markus; Rubio y Degrassi, Lleonard (Mathematisches Forschungsinstitut Oberwolfach, 2019-04-17)
      Let $A$ be a split finite-dimensional associative unital algebra over a field. The first main result of this note shows that if the Ext-quiver of $A$ is a simple directed graph, then $HH^1(A)$ is a solvable Lie algebra. ...
    • Plethysms, replicated Schur functions and series, with applications to vertex operators 

      [OWP-2010-12] Fauser, Bertfried; Jarvis, Peter D.; King, Ronald C. (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 ...
    • Positive Line Bundles Over the Irreducible Quantum Flag Manifolds 

      [OWP-2020-01] Díaz García, Fredy; Krutov, Andrey; Ó Buachalla, Réamonn; Somberg, Petr; Strung, Karen R. (Mathematisches Forschungsinstitut Oberwolfach, 2020-02-03)
      Noncommutative Kähler structures were recently introduced by the third author as a framework for studying noncommutative Kähler geometry on quantum homogeneous spaces. It was subsequently observed that the notion of a ...
    • A series of algebras generalizing the Octonions and Hurwitz-Radon Identity 

      [OWP-2010-10] Morier-Genoud, Sophie; Ovsienko, Valentin (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] Bodnarchuk, Lesya; Drozd, Jurij A.; Greuel, Gert-Martin (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 ...