scholarly journals On the Hopf algebra of functional graphs and differential algebras

1998 ◽  
Vol 183 (1-3) ◽  
pp. 119-140 ◽  
Author(s):  
M. Ginocchio
Keyword(s):  
Hopf Algebra ◽  
Differential Algebras

scholarly journals Hopf algebra methods in graph theory

1995 ◽  
Vol 101 (1) ◽  
pp. 77-90 ◽  
Author(s):  
William R. Schmitt
Keyword(s):  
Graph Theory ◽  
Hopf Algebra

scholarly journals CLASSICAL MARKOV PROCESSES FROM QUANTUM LÉVY PROCESSES

1999 ◽  
Vol 02 (01) ◽  
pp. 105-129 ◽  
Author(s):  
UWE FRANZ
Keyword(s):  
Markov Process ◽  
Hopf Algebra ◽  
Markov Processes ◽  
Lévy Processes ◽  
Sufficient Conditions ◽  
Markov Property ◽  
Vacuum State ◽  
Levy Processes ◽  
Quantum Process ◽  
Quantum Markov Processes

We show how classical Markov processes can be obtained from quantum Lévy processes. It is shown that quantum Lévy processes are quantum Markov processes, and sufficient conditions for restrictions to subalgebras to remain quantum Markov processes are given. A classical Markov process (which has the same time-ordered moments as the quantum process in the vacuum state) exists whenever we can restrict to a commutative subalgebra without losing the quantum Markov property.8 Several examples, including the Azéma martingale, with explicit calculations are presented. In particular, the action of the generator of the classical Markov processes on polynomials or their moments are calculated using Hopf algebra duality.

On A Multiplicativity up to Homotopy of the Gugenheim Map

2002 ◽  
Vol 9 (3) ◽  
pp. 549-566
Author(s):  
Z. Kharebava
Keyword(s):  
Cochain Complex ◽  
Differential Algebras ◽  
Graded Coalgebra

Abstract In the category of differential algebras with strong homotopy there is a Gugenheim's map {ρ 𝑖} : 𝐴* → 𝐶* from Sullivan's commutative cochain complex to the singular cochain complex of a space, which induces a differential graded coalgebra map of appropriate Bar constructions. Both (𝐵𝐴*, dBA , Δ,) and (𝐵𝐶*, dBC* , Δ,) carry multiplications. We show that the Gugenheim's map 𝐵{ρ 𝑖} : (𝐵𝐴*, dBA* , Δ,) → (𝐵𝐶*, dBC* , Δ,) is multiplicative up to homotopy with respect to these structures.

scholarly journals On integro-differential algebras

2014 ◽  
Vol 218 (3) ◽  
pp. 456-473 ◽  
Author(s):  
Li Guo ◽  
Georg Regensburger ◽  
Markus Rosenkranz
Keyword(s):  
Differential Algebras

scholarly journals Optimal embeddings of ultradistributions into differential algebras

2017 ◽  
Vol 186 (3) ◽  
pp. 407-438 ◽  
Author(s):  
Andreas Debrouwere ◽  
Hans Vernaeve ◽  
Jasson Vindas
Keyword(s):  
Differential Algebras
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