Cluster Algebras
Cluster algebras
... of cluster algebras, which has recently made its appearance on the mathematical scene, is developing rapidly and finding application in many different areas of ...on cluster algebras appeared ...
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Cluster Algebras and Mutation-Linear Algebra: Folding, Dominance, and the Orbifolds Model.
... Cluster algebras were introduced in [10] by Fomin and Zelevinsky, who noticed that the coordinate rings of many algebraic varieties carry a cluster algebra ...of cluster algebras which ...
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Reflection group presentations arising from cluster algebras.
... of cluster algebras of finite type from ...the cluster algebra, using generators and ...the cluster algebra, it follows that the group associated to any seed is isomorphic to this reflection ...
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Graded quantum cluster algebras of infinite rank as colimits
... In the second part, we generalise results of the second author ([11]) on colimits. In the classical case, one may show that the category Clus is neither complete nor cocomplete, that is, limits and colimits do not in ...
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Geometry & Cluster Algebras: Finite Type Classification & Double Bruhat Cells
... Which cluster algebras have finitely many clusters? (Theorem ...on cluster algebras (of ge- ometric type) called quotient and ...a cluster algebra of geometric type A is of finite type? ...
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Connected quantized Weyl algebras and quantum cluster algebras
... This paper is mostly in the context of noncommutative ring theory, in particular skew polynomial rings, classification of prime ideals and applications to quantum cluster algebras. The original motivation ...
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SKEIN AND CLUSTER ALGEBRAS OF MARKED SURFACES WITHOUT PUNCTURES FOR sl 3
... Here we recall some relations between the theory of cluster algebras [FZ02] and that of cluster varieties [FG09]. Although we mainly deal with (the quantum aspects of) the former in the text, we ...
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The geometry of Brauer graph algebras and cluster mutations.
... graph algebras which lies at the heart of this ...of cluster algebras and cluster ...tree algebras induced by the move on the dual graph induced by mutation of a diagonal in the ...
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Discrete Integrable Systems and Poisson Algebras From Cluster Maps
... Cluster algebras were first developed by Fomin and Zelevinsky more than a decade ago ...quantum algebras, Teichm¨ uller theory, discrete integrable systems and T- and ...for cluster ...
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Affine Lie Algebras, Vertex Operator Algebras and Combinatorial Identities
... Lie algebras and ultimately led to the discovery of new combinatorial identities (see for example [3] and [7]) and new algebraic structures such as vertex (operator) algebras (see for example [2], [8], ...
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On the Diagonals of Projections in Matrix Algebras Over Von Neumann Algebras
... Neumann algebras and use it to prove some new results on the one- sided ideals of von Neumann ...matrix algebras over an abelian C*-algebra is provided in chapter ...
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Lie algebras associated with quadratic forms and their applications to Ringel-Hall algebras
... In this paper, for any integral quadratic form q (2.1), we define by generators and relations, a Lie algebra L(q, r). For a positive definite form q, we describe a minimal set of relations defining L(q, r). Moreover we ...
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Approximate n Jordan ∗ derivations on C∗ algebras and JC∗ algebras
... 1. Ulam, SM: Problems in Modern Mathematics. Science ed. Wiley, New York (1940) (Chapter VI) 2. Hyers, DH: On the stability of the linear functional equation. Proc. Natl. Acad. Sci. USA 27, 222-224 (1941) 3. Aoki, T: On ...
10
On The Solvable Length of Associative Algebras, Matrix Groups, and Lie Algebras
... Lie algebras. There are many similarities between groups and Lie algebras, in particular between groups of order p n where p is prime, and nilpotent Lie algebras of dimension ...
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Relationship between Symmetric Brace Algebras and Pre-Lie Algebras
... pre-Lie algebras are more familiar to mathematicians than symmet- ric brace algebras, applications of these algebras seem to be more easily given by symmetric brace formulas ...
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On Liu algebras: a new composite structure of the BCL⁺ algebras and the semigroups
... BCL⁺ algebras are a very interesting area of research in the theory of algebraic systems in ...BCL⁺ algebras plays a central role in Liu algebras, and the semigroup is actually helping one important ...
16
On Companion B-algebras
... In 1999, J. Neggers and H. S. Kim [9], introduced the notion of d -algebra which is another generalization of BCK -algebra. In 2007, P. J. Allen, H. S. Kim and J. Neggers [3] developed the concept of companion d -algebra ...
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Quantum Boolean algebras
... In this section we study quantum Boolean algebras from a logical viewpoint. Propositional logic may be approached from a myriad of viewpoints. Here we take a revisionist approach bias towards the theory of operads ...
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On the anticommutativity in Leibniz algebras
... of algebras over a field of char- acteristic ...Leibniz algebras do not generally possess anticommutativity, as can be seen from their description given in ...
13
Knots and algebras
... such algebras has been known to a number of workers in the area, we feel that it is worth expounding here as it underlines the general strategy for computing invariants by working systematically with ...
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