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Quasi-linear Cycle Sets and the Retraction Problem for Set-theoretic Solutions of the Quantum Yang-Baxter Equation
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作者 Wolfgang Rump 《Algebra Colloquium》 SCIE CSCD 2016年第1期149-166,共18页
Cycle sets were introduced to reduce non-degenerate unitary Yang-Baxter maps to an algebraic system with a single binary operation. Every finite cycle set extends uniquely to a finite cycle set with a compatible abeli... Cycle sets were introduced to reduce non-degenerate unitary Yang-Baxter maps to an algebraic system with a single binary operation. Every finite cycle set extends uniquely to a finite cycle set with a compatible abelian group structure. Etingof et al. introduced affine Yang-Baxter maps. These are equivalent to cycle sets with a specific abelian group structure. Abelian group structures have also been essential to get partial results for the still unsolved retraction problem. We introduce two new classes of cycle sets with an underlying abelian group structure and show that they can be transformed into each other while keeping the group structure fixed. This leads to a proper extension of the retractibility conjecture and new evidence for its truth. 展开更多
关键词 quantum Yang-Baxter equation set-theoretical solution cycle set
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The double Ringel-Hall algebra on a hereditary abelian finitary length category
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作者 DOU RuJing LIU QunHua XIAO Jie 《Science China Mathematics》 SCIE 2011年第2期381-397,共17页
In this paper, we study the category H (ρ) of semi-stable coherent sheaves of a fixed slope ρ over a weighted projective curve. This category has nice properties: it is a hereditary abelian finitary length category.... In this paper, we study the category H (ρ) of semi-stable coherent sheaves of a fixed slope ρ over a weighted projective curve. This category has nice properties: it is a hereditary abelian finitary length category. We will define the Ringel-Hall algebra of H (ρ) and relate it to generalized Kac-Moody Lie algebras. Finally we obtain the Kac type theorem to describe the indecomposable objects in this category, i.e. the indecomposable semi-stable sheaves. 展开更多
关键词 Ringei-Hall algebra generalized Kac-Moody Lie algebra coherent sheaf semi-stability
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Some Open Problems Related to Creative Telescoping 被引量:3
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作者 CHEN Shaoshi KAUERS Manuel 《Journal of Systems Science & Complexity》 SCIE EI CSCD 2017年第1期154-172,共19页
Creative telescoping is the method of choice for obtaining information about definite sums or integrals. It has been intensively studied since the early 1990s, and can now be considered as a classical technique in com... Creative telescoping is the method of choice for obtaining information about definite sums or integrals. It has been intensively studied since the early 1990s, and can now be considered as a classical technique in computer algebra. At the same time, it is still a subject of ongoing research.This paper presents a selection of open problems in this context. The authors would be curious to hear about any substantial progress on any of these problems. 展开更多
关键词 Computer algebra creative telescoping differential algebra linear operators ore algebras symbolic integration symbolic summation.
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