ar X iv : m at h / 02 09 10 8 v 1 [ m at h . Q A ] 1 0 Se p 20 02 The hidden structure of Sl q ( 2 )
نویسنده
چکیده
In [1], we associate an oriented graph with each coalgebra and define the notion of (Markov) L-coalgebra, i.e. a k-vector space equipped with a left coproduct, ∆̃ and a right coproduct ∆, verifying the coassociativity breaking equation (∆̃⊗id)∆ = (id⊗∆)∆̃. The aim of this work is twofold. Firstly, we show that some coassociative coalgebras are closely related to Markov co-dialgebras, (i.e. Markov L-coalgebras verifying some additional conditions) whose associated oriented graphs are the De Bruijn graphs. Secondly we show that there exists a left-structure on the Hopf algebra Slq(2), (obtained graphically from the oriented graph of Slq(2)). This left structure is also a Hopf algebra whose left coproduct verifies the coassociativity breaking equation with the usual coproduct of Slq(2). This yields an example of an (achiral) L-Hopf algebra which cannot be thought in a markovian way. The gluing of these two oriented graphs of Slq(2) yields the 4-De Bruijn graph, which can be viewed as a Markov co-dialgebra. We finished this work by showing that the n-De Bruijn graph can be decomposed into n coassociative coalgebras. We yield also an example of coderivation.
منابع مشابه
ar X iv : m at h / 02 09 10 8 v 2 [ m at h . Q A ] 1 7 Se p 20 02 Paving the 4 - De - Bruijn graph with a
This paper is the following up of our work on coassociativity breaking and oriented graphs. Firstly, we show that there exists a left-structure on Slq(2) which is also a Hopf algebra and which is entangled by the coassociativity breaking equation to the usual one. Secondly, we show that the n-De Bruijn oriented graphs, viewed as Markov co-dialgebras, can be paved by n oriented graphs, viewed as...
متن کاملar X iv : m at h / 02 09 26 4 v 1 [ m at h . A G ] 2 0 Se p 20 02 1 Families of p - divisible groups with constant Newton polygon
Let X be a p-divisible group with constant Newton polygon over a normal noetherian scheme S. We prove that there exists an isogeny to X → Y such that Y admits a slope filtration. In case S is regular this was proved by N.Katz for dim S = 1 and by T.Zink for dim S ≥ 1.
متن کاملar X iv : m at h / 02 08 11 9 v 5 [ m at h . A G ] 1 1 Se p 20 02 GEOMETRY OF THE TETRAHEDRON SPACE
Let X be the space of all labeled tetrahedra in P. In [1] we constructed a smooth symmetric compactification X̃ of X. In this article we show that the complement X̃ r X is a divisor with normal crossings, and we compute the cohomology ring H(X̃ ;Q).
متن کاملar X iv : h ep - p h / 02 09 23 2 v 1 1 9 Se p 20 02 SEPARATION OF SOFT AND HARD PHYSICS IN DVCS
A model for deeply virtual Compton scattering, based on analytical light-cone hadron wave functions is presented and studied at energies currently accessible at Jefferson Laboratory and DESY. It is shown that poles and perpendicular vector components play an important role at Q 2 < 10 GeV 2. A Q 2 suppressed diagram has to be included at these low energies, but becomes negligible above 10 GeV 2...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2002