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On Universal Classes of Extremely Random Constant Time Hash Functions and Their TimeSpace Tradeoff
"... A family of functions F that map [0; n] 7! [0; n], is said to be hwise independent if any h points in [0; n] have an image, for randomly selected f 2 F , that is uniformly distributed. This paper gives both probabilistic and explicit randomized constructions of n ffl wise independent functions, ..."
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A family of functions F that map [0; n] 7! [0; n], is said to be hwise independent if any h points in [0; n] have an image, for randomly selected f 2 F , that is uniformly distributed. This paper gives both probabilistic and explicit randomized constructions of n ffl wise independent functions, ffl ! 1, that can be evaluated in constant time for the standard random access model of computation. Simple extensions give comparable behavior for larger domains. As a consequence, many probabilistic algorithms can for the first time be shown to achieve their expected asymptotic performance for a feasible model of computation. This paper also establishes a tight tradeoff in the number of random seeds that must be precomputed for a random function that runs in time T and is hwise independent. Categories and Subject Descriptors: E.2 [Data Storage Representation]: Hashtable representation; F.1.2 [Modes of Computation]: Probabilistic Computation; F2.3 [Tradepffs among Computational Measures]...
Some quantum analogues of solvable Lie groups, In: Geometry and analysis
, 1992
"... Introduction. In the papers [DK12],[DKP12] the quantized enveloping algebras introduced by Drinfeld and Jimbo have been studied in the case q = ε, a primitive lth root of 1 with l odd (cf. §2 for basic definitions). Let us only recall for the moment that such algebras are canonically constructed ..."
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Introduction. In the papers [DK12],[DKP12] the quantized enveloping algebras introduced by Drinfeld and Jimbo have been studied in the case q = ε, a primitive lth root of 1 with l odd (cf. §2 for basic definitions). Let us only recall for the moment that such algebras are canonically constructed starting from a Cartan matrix of finite type and in particular we
ABELIAN VARIETIES ASSOCIATED TO GAUSSIAN LATTICES
"... ABSTRACT. We associate to a unimodular lattice Γ, endowed with an automorphism of square −1, a principally polarized abelian variety AΓ = ΓR/Γ. We show that the configuration of iinvariant theta divisors of AΓ follows a pattern very similar to the classical theory of theta characteristics; as a con ..."
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ABSTRACT. We associate to a unimodular lattice Γ, endowed with an automorphism of square −1, a principally polarized abelian variety AΓ = ΓR/Γ. We show that the configuration of iinvariant theta divisors of AΓ follows a pattern very similar to the classical theory of theta characteristics; as a consequence we find that AΓ has a high number of vanishing thetanulls. When Γ = E8 we recover the 10 vanishing thetanulls of the abelian fourfold discovered by R. Varley.
ON POINTED HOPF ALGEBRAS WITH CLASSICAL WEYL GROUPS
, 902
"... Abstract. Many cases of infinite dimensional Nichols algebras of irreducible YetterDrinfeld modules over classical Weyl groups are found. It is proved that except a few cases Nichols algebras of reducible YetterDrinfeld modules over classical Weyl groups are infinite dimensional. Some finite dimen ..."
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Abstract. Many cases of infinite dimensional Nichols algebras of irreducible YetterDrinfeld modules over classical Weyl groups are found. It is proved that except a few cases Nichols algebras of reducible YetterDrinfeld modules over classical Weyl groups are infinite dimensional. Some finite dimensional Nichols algebras of YetterDrinfeld modules over classical Weyl groups are given. This article is to contribute to the classification of finitedimensional complex pointed Hopf algebras with Weyl groups of classical type. Weyl groups are very important in the theories of Lie groups, Lie algebras and algebraic groups. The classification of finite dimensional pointed Hopf algebra with finite abelian groups has been finished (see [He06,
THE CHARACTER TABLES OF CENTRALIZERS IN WEYL GROUP OF E8 V
, 804
"... Abstract. To classify the finite dimensional pointed Hopf algebras with Weyl group G of E8, we obtain the representatives of conjugacy classes of G and all character tables of centralizers of these representatives by means of software GAP. In this paper we only list character table 95–112. 2000 Math ..."
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Abstract. To classify the finite dimensional pointed Hopf algebras with Weyl group G of E8, we obtain the representatives of conjugacy classes of G and all character tables of centralizers of these representatives by means of software GAP. In this paper we only list character table 95–112. 2000 Mathematics Subject Classification: 16W30, 68M07
THE CHARACTER TABLES OF CENTRALIZERS IN WEYL GROUPS OF E6, E7, F4, G2
, 804
"... Abstract. To classify the finite dimensional pointed Hopf algebras with Weyl group G of E6, E7, F4, G2, we obtain the representatives of conjugacy classes of G and all character tables of centralizers of these representatives by means of software GAP. 2000 Mathematics Subject Classification: 16W30, ..."
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Abstract. To classify the finite dimensional pointed Hopf algebras with Weyl group G of E6, E7, F4, G2, we obtain the representatives of conjugacy classes of G and all character tables of centralizers of these representatives by means of software GAP. 2000 Mathematics Subject Classification: 16W30, 68M07
On Pointed Hopf Algebras with Weyl Groups of Exceptional Type
, 804
"... All −1type pointed Hopf algebras and central quantum linear spaces with Weyl groups of exceptional type are found. It is proved that every non −1type pointed Hopf algebra with real G(H) is infinite dimensional and every central quantum linear space over finite group is finite dimensional. It is pr ..."
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All −1type pointed Hopf algebras and central quantum linear spaces with Weyl groups of exceptional type are found. It is proved that every non −1type pointed Hopf algebra with real G(H) is infinite dimensional and every central quantum linear space over finite group is finite dimensional. It is proved that except a few cases Nichols algebras of reducible YetterDrinfeld modules over Weyl groups of exceptional type are infinite dimensional.
THE CHARACTER TABLES OF CENTRALIZERS IN WEYL GROUP OF E8 III
, 804
"... Abstract. To classify the finite dimensional pointed Hopf algebras with Weyl group G of E8, we obtain the representatives of conjugacy classes of G and all character tables of centralizers of these representatives by means of software GAP. In this paper we only list character table 47–64. ..."
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Abstract. To classify the finite dimensional pointed Hopf algebras with Weyl group G of E8, we obtain the representatives of conjugacy classes of G and all character tables of centralizers of these representatives by means of software GAP. In this paper we only list character table 47–64.