斐波那契数列在表示论中的几类范畴化及其在复杂度上的应用  

Some Examples of Categorification of Fibonacci Sequence in Representation Theory and in the Application of Complexity

作　　者：罗德仁 周潘岳 LUO Dereu;ZHOU Panyue(College of Mathematics,Hunan Institute of Science and Technology,Yueyang,Hman,4^4006,P.R.China)

机构地区：[1]湖南理工学院数学学院,岳阳湖南414006

出　　处：《数学进展》2019年第1期45-52,共8页Advances in Mathematics（China）

基　　金：国家自然科学基金(Nos.11671126;11671221);湖南省自然科学基金(Nos.2018JJ3204;2018JJ3205)

摘　　要：本文给出斐波那契数列和广义斐波那契数列在代数表示论中的范畴化的几个例子.作为应用,利用斐波那契数列的指数增长性的方法证明外代数的斜群代数的有限生成模范畴modΛV*G的子范畴并不一定保持复杂度.In this paper,several examples of categorifications of Fibonacci sequence and generalized Fibonacci sequence appeared in representation theory are presented.We also show by example that there exists a subcategory of mod AV*G which does not keep the complexity via the exponential of the formula of general term of Fibonacci sequence.

关 键 词：斐波那契数列 范畴化 复杂度 

分 类 号：O154.2[理学—数学]