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pro vyhledávání: '"Lenzing, Helmut"'
This present paper is devoted to the study of a class of Nakayama algebras $N_n(r)$ given by the path algebra of the equioriented quiver $\mathbb{A}_n$ subject to the nilpotency degree $r$ for each sequence of $r$ consecutive arrows. We show that the
Externí odkaz:
http://arxiv.org/abs/2112.15587
Autor:
Lenzing, Helmut
This article has the following aims: (1) Extend the notion of fuchsian singularities (of first kind) to base fields of arbitrary characteristic. (2) Discuss their relationship to mathematical objects of a different nature. (3) Provide a purely ring-t
Externí odkaz:
http://arxiv.org/abs/1909.10362
Autor:
Lenzing, Helmut
We present a largely self contained account on the K-theory of a weighted smooth projective curve over an algebraically closed field. In particular, we discuss the weighted version of divisor theory, Euler form, and Riemann-Roch theorem. This include
Externí odkaz:
http://arxiv.org/abs/1702.03445
Autor:
Lenzing, Helmut
For the base field of complex numbers we discuss the relationship between categories of coherent sheaves on compact Riemann surfaces and categories of coherent sheaves on weighted smooth projective curves. This is done by bringing back to life an old
Externí odkaz:
http://arxiv.org/abs/1612.02960
Publikováno v:
Colloq. Math. 140 (2015), 239-278
Working over an algebraically closed field $k$ of any characteristic, we determine the matrix factorizations for the --- suitably graded --- triangle singularities $f=x^a+y^b+z^c$ of domestic type, that is, we assume that $(a,b,c)$ are integers at le
Externí odkaz:
http://arxiv.org/abs/1507.07832
Canonical algebras, introduced by C.M. Ringel in 1984, play an important role in the representation theory of finite dimensional algebras. They are equipped with a large contact surface to many further mathematical subjects like function theory, 3-ma
Externí odkaz:
http://arxiv.org/abs/1208.3761
We investigate the triangle singularity $f=x^a+y^b+z^c$, or $S=k[x,y,z]/(f)$, attached to a weighted projective line $X$ given by the weight triple $(a,b,c)$. We investigate the stable category of vector bundles on $X$ obtained from the vector bundle
Externí odkaz:
http://arxiv.org/abs/1203.5505
Publikováno v:
J. Reine Angew. Math. 685 (2013), 33-71
We show a surprising link between singularity theory and the invariant subspace problem of nilpotent operators as recently studied by C. M. Ringel and M. Schmidmeier, a problem with a longstanding history going back to G. Birkhoff. The link is establ
Externí odkaz:
http://arxiv.org/abs/1002.3797
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We give a summary on spectral techniques for finite dimensional algebras and study its link to singularity theory. In particular, we offer a contribution to the categorification of the Milnor lattice of two-dimensional singularities through triangula
Externí odkaz:
http://arxiv.org/abs/0805.1018