论文标题
在非中心frobenius代数上
On non-counital Frobenius algebras
论文作者
论文摘要
Frobenius代数是有限维代数$ a $，配备了共同点的，顾问合作地图$δ$，这是$ a $ a-bimodule地图。在这里，我们研究了Frobenius代数的概括：有限维自注（Quasi-Frobenius）代数代数的概括。我们表明，包括有限维弱的HOPF代数在内的大量此类代数，配备了非零地图$δ$，不一定是Counital。我们还猜想，这种共同的结构通常适用于自我注射代数。
A Frobenius algebra is a finite-dimensional algebra $A$ which comes equipped with a coassociative, counital comultiplication map $Δ$ that is an $A$-bimodule map. Here, we examine comultiplication maps for generalizations of Frobenius algebras: finite-dimensional self-injective (quasi-Frobenius) algebras. We show that large classes of such algebras, including finite-dimensional weak Hopf algebras, come equipped with a nonzero map $Δ$ as above that is not necessarily counital. We also conjecture that this comultiplicative structure holds for self-injective algebras in general.
