Categorification of Hopf algebras of rooted trees
نویسندگان
چکیده
منابع مشابه
Combinatorics of Rooted Trees and Hopf Algebras
We begin by considering the graded vector space with a basis consisting of rooted trees, with grading given by the count of non-root vertices. We define two linear operators on this vector space, the growth and pruning operators, which respectively raise and lower grading; their commutator is the operator that multiplies a rooted tree by its number of vertices, and each operator naturally assoc...
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In [8], Dirk Kreimer discovered the striking fact that the process of renormalization in quantum field theory may be described, in a conceptual manner, by means of certain Hopf algebras (which depend on the chosen renormalization scheme). A toy model was studied in detail by Alain Connes and Dirk Kreimer in [3]; the Hopf algebra which occurs, denoted by HR, is the polynomial algebra in an infin...
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Let K be any unital commutative Q-algebra and W any non-empty subset of N. Let z = (z1, . . . , zn) be commutative or noncommutative free variables and t a formal central parameter. Let D〈〈z〉〉 (α ≥ 1) be the unital algebra generated by the differential operators ofK〈〈z〉〉 which increase the degree in z by at least α− 1 and A [α] t 〈〈z〉〉 the group of automorphisms Ft(z) = z−Ht(z) of K[[t]]〈〈z〉〉 w...
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We find a formula to compute the number of the generators, which generate the n-filtered space of Hopf algebra of rooted trees, i.e. the number of equivalent classes of rooted trees with weight n. Applying Hopf algebra of rooted trees, we show that the analogue of Andruskiewitsch and Schneider’s Conjecture is not true. The Hopf algebra of rooted trees and the enveloping algebra of the Lie algeb...
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A tree T of order n is called k-placement if there are k edge-disjoint copies of T into K_{n}. In this paper we prove some results about 4-placement of rooted trees.
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ژورنال
عنوان ژورنال: Open Mathematics
سال: 2013
ISSN: 2391-5455
DOI: 10.2478/s11533-012-0152-1