论文标题
$λ$ -TD代数，广义洗牌产品和左Counital Hopf代数
$λ$-TD algebras, generalized shuffle products and left counital Hopf algebras
论文作者
论文摘要
操作代数理论在数学和物理学中发挥了关键作用。在本文中，我们引入了$λ$ -TD代数，适当地包括rota-baxter代数和TD-Algebra。在交换代数上的明确结构$λ$ -TD代数是通过广义的洗牌产品获得的，称为$λ$ -td Shuffle产品。然后，我们证明免费的$λ$ -TD代数通过合适的1 cocycle条件具有左Counital Bialgera结构。此外，每个连接的滤波后的双子骨都是Hopf代数的经典结果。鉴于此结果，我们最终证明了自由交换$λ$ -td代数上的左圆圆锥形bialgebra已连接并过滤，因此是左Counital Hopf代数。
The theory of operated algebras has played a pivotal role in mathematics and physics. In this paper, we introduce a $λ$-TD algebra that appropriately includes both the Rota-Baxter algebra and the TD-algebra. The explicit construction of free commutative $λ$-TD algebra on a commutative algebra is obtained by generalized shuffle products, called $λ$-TD shuffle products. We then show that the free commutative $λ$-TD algebra possesses a left counital bialgera 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 $λ$-TD algebra is connected and filtered, and thus is a left counital Hopf algebra.
