Zobrazeno 1 - 10
of 114
pro vyhledávání: '"Schröer, Jan"'
We study semicontinuous maps on varieties of modules over finite-dimensional algebras. We prove that truncated Euler maps are upper or lower semicontinuous. This implies that $g$-vectors and $E$-invariants of modules are upper semicontinuous. We also
Externí odkaz:
http://arxiv.org/abs/2302.02085
We realize Derksen-Weyman-Zelevinsky's mutations of representations as densely-defined regular maps on representation spaces, and study the generic values of Caldero-Chapoton functions with coefficients, giving, for instance, a sufficient combinatori
Externí odkaz:
http://arxiv.org/abs/2007.05483
Publikováno v:
Selecta Math. (N.S.) 28 (2022), no. 1, Paper No. 8, 78 pp
We study the affine schemes of modules over gentle algebras. We describe the smooth points of these schemes, and we also analyze their irreducible components in detail. Several of our results generalize formerly known results, e.g. by dropping acycli
Externí odkaz:
http://arxiv.org/abs/2005.01073
Akademický článek
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Publikováno v:
Math. Z. 295 (2020), no. 3-4, 1245-1277
Let $C$ be a symmetrizable generalized Cartan matrix with symmetrizer $D$ and orientation $\Omega$. In previous work we associated an algebra $H$ to this data, such that the locally free $H$-modules behave in many aspects like representations of a he
Externí odkaz:
http://arxiv.org/abs/1812.09663
Publikováno v:
J. Algebra 558 (2020), 411-422
We show that in case a cluster algebra coincides with its upper cluster algebra and the cluster algebra admits a grading with finite dimensional homogeneous components, the corresponding Berenstein-Zelevinsky quantum cluster algebra can be viewed as
Externí odkaz:
http://arxiv.org/abs/1807.09826
Autor:
Bobiński, Grzegorz, Schröer, Jan
We call a finite-dimensional K-algebra A geometrically irreducible if for all d all connected components of the affine scheme of d-dimensional A-modules are irreducible. We prove that a geometrically irreducible algebra with exactly two simple module
Externí odkaz:
http://arxiv.org/abs/1801.03677
Autor:
Bobiński, Grzegorz, Schröer, Jan
We call a finite-dimensional K-algebra A geometrically irreducible if for all d, all connected components of the affine scheme of d-dimensional A-modules are irreducible. We show that the geometrically irreducible algebras without loops (this include
Externí odkaz:
http://arxiv.org/abs/1709.05841
Publikováno v:
Proc. Lond. Math. Soc. (3) 117 (2018), no. 1, 125-148
We generalize the Caldero-Chapoton formula for cluster algebras of finite type to the skew-symmetrizable case. This is done by replacing representation categories of Dynkin quivers by categories of locally free modules over certain Iwanaga-Gorenstein
Externí odkaz:
http://arxiv.org/abs/1704.06438
Publikováno v:
Selecta Math. (N.S.) 24 (2018), no. 4, 3283-3348
We generalize Lusztig's nilpotent varieties, and Kashiwara and Saito's geometric construction of crystal graphs from the symmetric to the symmetrizable case. We also construct semicanonical functions in the convolution algebras of generalized preproj
Externí odkaz:
http://arxiv.org/abs/1702.07570