Non-simply-laced Clusters of Finite Type via Frobenius Morphism
نویسنده
چکیده
By showing the compatibility of folding almost positive roots and folding cluster categories, we prove that there is a one-to-one correspondence between seeds and tilting seeds in non-simply-laced finite cases.
منابع مشابه
Frobenius Morphisms of Noncommutative Blowups
We define the Frobenius morphism of certain class of noncommutative blowups in positive characteristic. Thanks to a nice property of the class, the defined morphism is always flat. Therefore we say that the noncommutative blowups in this class are Kunz regular. One of such blowups is the one associated to a regular Galois alteration. From de Jong’s theorem, we see that for every variety over an...
متن کاملBmw Algebras of Simply Laced Type
It is known that the recently discovered representations of the Artin groups of type An, the braid groups, can be constructed via BMW algebras. We introduce similar algebras of type Dn and En which also lead to the newly found faithful representations of the Artin groups of the corresponding types. We establish finite dimensionality of these algebras. Moreover, they have ideals I1 and I2 with I...
متن کاملRoot Systems and the Quantum Cohomology of Ade Resolutions
We compute the C∗-equivariant quantum cohomology ring of Y , the minimal resolution of the DuVal singularity C/G where G is a finite subgroup of SU(2). The quantum product is expressed in terms of an ADE root system canonically associated to G. We generalize the resulting Frobenius manifold to non-simply laced root systems to obtain an n parameter family of algebra structures on the affine root...
متن کاملS-matrices of non-simply laced affine Toda theories by folding
The exact factorisable quantum S-matrices are known for simply laced as well as non-simply laced affine Toda field theories. Non-simply laced theories are obtained from the affine Toda theories based on simply laced algebras by folding the corresponding Dynkin diagrams. The same process, called classical ‘reduction’, provides solutions of a non-simply laced theory from the classical solutions w...
متن کامل0 M ay 2 00 6 BGP - reflection functors and cluster combinatorics ∗
We define Bernstein-Gelfand-Ponomarev reflection functors in the cluster categories of hereditary algebras. They are triangle equivalences which provide a natural quiver realization of the ”truncated simple reflections” on the set of almost positive roots Φ≥−1 associated to a finite dimensional semisimple Lie algebra. Combining with the tilting theory in cluster categories developed in [4], we ...
متن کامل