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- W4313332017 abstract "Operated algebras, that is, algebras equipped with linear operators, have important applications in mathematics and physics. Two primary instances of operated algebras are the Rota–Baxter algebra and TD-algebra. In this paper, we introduce a [Formula: see text]-TD algebra that includes both the Rota–Baxter algebra and the TD-algebra. The explicit construction of free commutative [Formula: see text]-TD algebra on a commutative algebra is obtained by a generalized shuffle product, called the [Formula: see text]-TD shuffle product. We then show that the free commutative [Formula: see text]-TD algebra possesses a left counital bialgebra structure by means of a suitable 1-cocycle condition. Furthermore, the classical result that every connected filtered bialgebra is a Hopf algebra, is extended to the context of left counital bialgebras. Given this result, we finally prove that the left counital bialgebra on the free commutative [Formula: see text]-TD algebra is connected and filtered, and thus is a left counital Hopf algebra." @default.
- W4313332017 created "2023-01-06" @default.
- W4313332017 creator A5028584647 @default.
- W4313332017 creator A5081616736 @default.
- W4313332017 date "2023-01-21" @default.
- W4313332017 modified "2023-10-18" @default.
- W4313332017 title "λ-TD algebras, generalized shuffle products and left counital Hopf algebras" @default.
- W4313332017 doi "https://doi.org/10.1142/s0219498824500993" @default.
- W4313332017 hasPublicationYear "2023" @default.
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