Relation algebras give rise to partial algebras on maps, which are generalized to partial algebras on polymaps while preserving the properties of relation union and composition. A polymap is defined as a map with ever...Relation algebras give rise to partial algebras on maps, which are generalized to partial algebras on polymaps while preserving the properties of relation union and composition. A polymap is defined as a map with every point in the domain associated with a special set of maps. Polymaps can be represented as small subcategories of Set＊, the category of pointed sets. Map composition and the counterpart of relation union for maps are generalized to polymap composition and sum. Algebraic structures and categories of polymaps are investigated. Polymaps present the unique perspective of an algebra that can retain many of its properties when its elements （maps） are augmented with collections of other elements.展开更多
The author constructs the Casimir element of Hall algebras. By the method of Gabber-Kac theorem (see [4]), it is proved that the Serre relations are the defining relations in composition algebra.
文摘Relation algebras give rise to partial algebras on maps, which are generalized to partial algebras on polymaps while preserving the properties of relation union and composition. A polymap is defined as a map with every point in the domain associated with a special set of maps. Polymaps can be represented as small subcategories of Set＊, the category of pointed sets. Map composition and the counterpart of relation union for maps are generalized to polymap composition and sum. Algebraic structures and categories of polymaps are investigated. Polymaps present the unique perspective of an algebra that can retain many of its properties when its elements （maps） are augmented with collections of other elements.
文摘The author constructs the Casimir element of Hall algebras. By the method of Gabber-Kac theorem (see [4]), it is proved that the Serre relations are the defining relations in composition algebra.
基金Supported by the National Natural Science Foundation of China under Grant Nos.10571112, 60673105(国家自然科学基金)the Teaching and Research Award Program for Outstanding Young Teachers in Higher Education Institutions of MOE, China(高等学校优秀 青年教师教学科研奖励计划)the National Basic Research Program of China under Grant No.2002CB312200(国家重点基础研究发展 计划(973))
