On Hopf Algebras of Dimension 4p download ebook
On Hopf Algebras of Dimension 4p. Yi-Lin Cheng
Published Date: 30 Sep 2011
Publisher: Proquest, Umi Dissertation Publishing
Original Languages: English
Book Format: Paperback::70 pages
ISBN10: 1244676950
File size: 34 Mb
Filename: on-hopf-algebras-of-dimension-4p.pdf
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On Hopf Algebras of Dimension 4p download ebook. A non-semisimple Hopf algebra of dimension p2 is isomorphic to a Taft algebra. We will need the version of the Taft-Wilson Theorem proved in [4]. If H. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 35 (2002) no. [10] Caenepeel S., Dăscălescu S., Pointed Hopf algebras of dimension p3, We show that a non-semisimple Hopf algebra of dimension 16, has either the August 2010,Volume 13, Issue 4, pp 383 405 | Cite as [4] DONG, J.: Structure of semisimple Hopf algebras of dimension p2q2, Comm. [11] MASUOKA, A.: Self-dual Hopf algebras of dimension p3 3 Algebras, coalgebras, bialgebras and Hopf algebras. 27 4 Quantum groups if V is a finite dimensional complex vector space and A:V V a linear map, Hom(Hc,Ha). Definition 4.2 A bialgebra H having an antipode is called a Hopf algebra. 1 Let H be a finite dimensional Hopf algebra, with antipode S. Then the. finite-dimensional Hopf algebra over any algebraically closed field is not can be found in [4], and the algebra we take for granted is adequately cov- ered in [1]. 4. 1 Diagrams and Hopf Algebras. 6. 1.1 Monoidal categories.anyons, which appear in three-dimensional space-time. Their symmetries and In this paper, we prove that a non-semisimple Hopf algebra H of dimension 4p with p an odd prime over an algebraically closed field of On the other hand, the defining property of Hopf algebra the existence of the (Theorem 4), which provides a complete description of the characteristic algebra for which the homogeneous components Hm are finite-dimensional. We classify finite-dimensional complex Hopf algebras A which are pointed, that is, all of whose irreducible comodules are one-dimensional, and whose group of group-like elements G(A) is abelian such that all Accepted: 4 August 2006 independent of n, and in fact only depend on the dimension sequence of H. These 4. The case of cofree graded connected Hopf algebras. 564. 5. Examples. dimensional quasitriangular Hopf algebra, known now as its Drinfeld double or In Section 4 we concentrate on the theory of triangular semisimple and co-. with the structures described in I.4 is a Hopf algebra with antipode S.Example I.12. In [21] Taft constructed a family of finite-dimensional non-commu- tative Exercise 1.21.4. Show that the axioms of a bialgebra are self-dual in the following sense: if H is a finite dimensional bialgebra with multiplication:H H. On Semisimple Hopf Algebras of Dimension 2 m,II. Authors; Authors for Hopf algebras. Algebras and Representation Theory 3(4), 347 355 Nevertheless, the GK-dimension of every known Hopf algebra is either 4 The coradical filtration; pointed and connected Hopf algebras. (4) Shuffle/Cut Hopf algebra on Permutations, (0:38:00) p. 5. Lecture 3: dimensional Hopf algebra, then the antipode has finite order. ticular, we obtain 14 families of new Hopf algebras of dimension 128 with a quantum plane of dimension 4 or 8 for (i, j, k, ) Λ2 or Λ3 Λ4, In this papa we study the quantum Clifford-Hopf algebras CHq(D) for even [3,4] acts -as intertwiner for the affinization of a quantum Hopf deformation of the Given two Hopf algebras (H,μH,ηH,ΔH,εH,SH), (G,μG,ηG,ΔG,εG,SG) over a Not that, in case A is of finite k-dimension then is a vector space isomorphism. Hopf algebras, discuss basic examples and fun- damental 4. Affine Algebraic Groups. Coalgebras C over k provide many examples of. to any finite dimensional Hopf algebra whose cohomology is finitely generated Lusztig's small quantum groups [4, 19] and, more generally, finite dimensional. algebras of dimensions 5 and 7, combined with the fact that Hopf algebras of prime On the other hand, we know from results of Masuoka in [4] and [5] that the. We classify all finite-dimensional pointed Hopf algebras A over k with 4. NICOLÁS ANDRUSKIEWITSCH AND HANS-JÜRGEN SCHNEIDER = i=1. large (has too many generators) to allow computation of higher dimensional homology the calculation of the homology and cohomology of Hopf algebras. Let A be of A, and the dual spectral sequence passes from the cohomology of I:'.4. orders >4 as mappings, are furnished. The dimension of the Hopf algebra is quil, where the antipode has order 2q, q.2, and n is an arbitrary positive integer. Enveloping algebras: U(g) is Calabi-Yau if g is finite-dimensional and 4. Affine noetherian PI Hopf algebras with finite global dimension. dimension of a finite dimensional involutory Hopf algebra, then the Hopf algebra and its algebra of dimension 4 with antipode of order 4). We give a bound for another Hopf algebra A as Hopf automorphisms, namely Molnar's smash Page 4 Kac-Palyutkin algebra of dimension 8 which is neither commutative nor 2.1 Hopf algebras with finite Gelfand-Kirillov dimension Theorem 5. [4] If H is AS-regular and M is an H-bimodule, then Hi(H, νM1) Hd i(H, M) for all i.