Browsing by MSC "15"
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Abstract Bivariant Cuntz Semigroups
[OWP201704] (Mathematisches Forschungsinstitut Oberwolfach, 20170213)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 ... 
A Deformed Quon Algebra
[OWP201811] (Mathematisches Forschungsinstitut Oberwolfach, 20180625)The quon algebra is an approach to particle statistics in order to provide a theory in which the Pauli exclusion principle and Bose statistics are violated by a small amount. The quons are particles whose annihilation and ... 
Generalized Vector Cross Products and Killing Forms on Negatively Curved Manifolds
[OWP201817] (Mathematisches Forschungsinstitut Oberwolfach, 20180717)Motivated by the study of Killing forms on compact Riemannian manifolds of negative sectional curvature, we introduce the notion of generalized vector cross products on $\mathbb{R}^n$ and give their classification. Using ... 
Geometry of Free Loci and Factorization of Noncommutative Polynomials
[OWP201723] (Mathematisches Forschungsinstitut Oberwolfach, 20171002)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 ... 
Infeasibility certificates for linear matrix inequalities
[OWP201128] (Mathematisches Forschungsinstitut Oberwolfach, 20110525)Farkas' lemma is a fundamental result from linear programming providing linear certi cates for infeasibility of systems of linear inequalities. In semidefinite programming, such linear certificates only exist for strongly ... 
Invariant Fourforms and Symmetric Pairs
[OWP201203] (Mathematisches Forschungsinstitut Oberwolfach, 20120424)We give criteria for real, complex and quaternionic representations to define $s$representations, focusing on exceptional Lie algebras defined by spin representations. As applications, we obtain the classification of ... 
Low rank differential equations for hamiltonian matrix nearness problems
[OWP201301] (Mathematisches Forschungsinstitut Oberwolfach, 20130208)For a Hamiltonian matrix with purely imaginary eigenvalues, we aim to determine the nearest Hamiltonian matrix such that so me or all eigenvalues leave the imaginary axis. Conversely, for a Hamiltonian matrix with all ... 
The Magic Square of Reflections and Rotations
[OWP201813] (Mathematisches Forschungsinstitut Oberwolfach, 20180701)We show how Coxeter’s work implies a bijection between complex reflection groups of rank two and real reflection groups in 0(3). We also consider this magic square of reflections and rotations in the framework of Clifford ... 
Nonstationary multivariate subdivision: joint spectral radius and asymptotic similarity
[OWP201320] (Mathematisches Forschungsinstitut Oberwolfach, 20131029)In this paper we study scalar multivariate nonstationary subdivision schemes with a general integer dilation matrix. We present a new numerically efficient method for checking convergence and Hölder ... 
On the Derived Category of Grassmannians in Arbitrary Characteristic
[OWP201324] (Mathematisches Forschungsinstitut Oberwolfach, 20131209)In this paper we consider Grassmannians in arbitrary characteristic. Generalizing Kapranov's wellknown characteristiczero results we construct dual exceptional collections on them (which are however not strong) as well ... 
A series of algebras generalizing the Octonions and HurwitzRadon Identity
[OWP201010] (Mathematisches Forschungsinstitut Oberwolfach, 2010)We study nonassociative 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 ... 
Supertropical linear algebra
[OWP201014] (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
[OWP201020] (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
[OWP201327] (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 ringtheoretic case, the companion ... 
Yet another algorithm for the symmetric eigenvalue problem
[OWP201602] (Mathematisches Forschungsinstitut Oberwolfach, 20160510)In this paper we present a new algorithm for solving the symmetric matrix eigenvalue problem that works by first using a Cayley transformation to convert the symmetric matrix into a unitary one and then uses Gragg’s ...