In this paper, by using the notion of convolution types we introduce symmetric and non-symmetric convolution type \(\hbox {C}^*\)-algebras. It is shown that any (exact) convolution type induces a (an exact) functor on the category of \(\hbox {C}^*\)-algebras. In particular, any group induces a convolution type and a functor on the category of \(\hbox {C}^*\)-algebras. It is also shown that discrete crossed product of \(\hbox {C}^*\)-algebras and discrete inverse semigroup \(\hbox {C}^*\)-algebras can be considered as convolution type \(\hbox {C}^*\)-algebras.

中文翻译：

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卷积类型$$ \ hbox {C} ^ * $$ C ∗-代数

在本文中，通过使用卷积类型的概念，我们介绍了对称和非对称卷积类型\（\ hbox {C} ^ * \）-代数。结果表明，任何（精确）卷积类型都会在\（\ hbox {C} ^ * \）-代数的类别中诱导一个（精确）函子。特别是，任何组都在\（\ hbox {C} ^ * \）-代数的类别中引发卷积类型和函子。还显示\（\ hbox {C} ^ * \）-代数和离散逆半群\（\ hbox {C} ^ * \）-代数的离散叉积可以视为卷积类型\（\ hbox { C} ^ * \）-代数。