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Expressions of algebra elements and transcendental noncommutative calculus
, 2008
"... Abstract Ideas from deformation quantization are applied to deform the expression of elements of an algebra. Extending these ideas to certain transcendental elements implies that 1 i�uv in the Weyl algebra is naturally viewed as an indeterminate living in a discrete set N+ 1 2 or −(N+1 ..."
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Cited by 3 (0 self)
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Abstract Ideas from deformation quantization are applied to deform the expression of elements of an algebra. Extending these ideas to certain transcendental elements implies that 1 i�uv in the Weyl algebra is naturally viewed as an indeterminate living in a discrete set N+ 1 2 or −(N+1
TRANSCENDENTAL PHILOSOPHY AND QUANTUM PHYSICS
"... Abstract: In the Critique of Pure Reason Kant argues that the empirical knowledge of the world depends on a priori conditions of human sensibility and understanding, i. e., our capacities of sense experience and concept formation. The objective knowledge presupposes, on one hand, space and time as a ..."
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the classical physics. The aim of this work is firstly to show the Kantian implications on Bohr’s interpretation of quantum phenomena and secondly to provide an overview of the key elements for understanding the transcendental locus of ordinary language in the quantum mechanics context, in order to give support
TRANSCENDENTAL BRAUER ELEMENTS VIA DESCENT ON ELLIPTIC SURFACES
"... Transcendental Brauer elements are notoriously difficult to compute. Work of Wittenberg, and later, Ieronymou, gives a method for computing 2torsion transcendental classes on surfaces that have a genus 1 fibration with rational 2torsion in the Jacobian fibration. We use ideas from a descent paper ..."
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Transcendental Brauer elements are notoriously difficult to compute. Work of Wittenberg, and later, Ieronymou, gives a method for computing 2torsion transcendental classes on surfaces that have a genus 1 fibration with rational 2torsion in the Jacobian fibration. We use ideas from a descent paper
FullDiversity, HighRate SpaceTime Block Codes from Division Algebras
 IEEE TRANS. INFORM. THEORY
, 2003
"... We present some general techniques for constructing fullrank, minimaldelay, rate at least one spacetime block codes (STBCs) over a variety of signal sets for arbitrary number of transmit antennas using commutative division algebras (field extensions) as well as using noncommutative division algeb ..."
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Cited by 177 (55 self)
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's code is just a special case of the construction using representation over maximal cyclic subfields and we observe certain algebraic uniqueness characteristics of it. Also, we discuss a general principle for constructing cyclic division algebras using the th root of a transcendental element and study
GALOIS THEORY, MOTIVES AND TRANSCENDENTAL NUMBERS.
, 805
"... ABSTRACT. From its early beginnings up to nowadays, algebraic number theory has evolved in symbiosis with Galois theory: indeed, one could hold that it consists in the very study of the absolute Galois group of the field of rational numbers. Nothing like that can be said of transcendental number the ..."
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Cited by 7 (0 self)
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ABSTRACT. From its early beginnings up to nowadays, algebraic number theory has evolved in symbiosis with Galois theory: indeed, one could hold that it consists in the very study of the absolute Galois group of the field of rational numbers. Nothing like that can be said of transcendental number
TRANSCENDENTAL VALUES OF CLASS GROUP LFunctions, II
, 2012
"... Let K be an imaginary quadratic field and f an integral ideal. Denote by Cl(f) the ray class group of f. For every nontrivial character χ of Cl(f), we show that L(1,χ)/π is transcendental. If f = f, then complex conjugation acts on the character group of Cl(f). Denoting by Ĉl(f)+ the orbits of the ..."
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Cited by 5 (3 self)
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of the group of characters, we show that the values L(1,χ)asχ ranges over elements of Ĉl(f)+ are linearly independent over Q. We give applications of this result to the study of transcendental values of Petersson inner products and certain special values of Artin Lseries attached to dihedral extensions.
EVERY TRANSCENDENTAL OPERATOR HAS A NONTRIVIAL INVARIANT SUBSPACE
, 901
"... Abstract. In this paper, to solve the invariant subspace problem, contraction operators are classified into three classes; (Case 1) completely nonunitary contractions with a nontrivial algebraic element, (Case 2) completely nonunitary contractions without a nontrivial algebraic element, or (Case ..."
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Abstract. In this paper, to solve the invariant subspace problem, contraction operators are classified into three classes; (Case 1) completely nonunitary contractions with a nontrivial algebraic element, (Case 2) completely nonunitary contractions without a nontrivial algebraic element, or (Case
i THE TRANSCENDENTAL PART OF THE REGULATOR MAP FOR K1 ON A MIRROR FAMILY
, 2001
"... We compute the transcendental part of the normal function corresponding to the Deligne class of a cycle in K1 of a mirror family of quartic K 3 surfaces. The resulting multivalued function does not satisfy the hypergeometric differential equation of the periods, and we conclude that the cycle is in ..."
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surface X. It was conjectured by H. Esnault around 1995 that certain elements in this group can be detected in the transcendental part of the Deligne cohomology group H 3 D (X, Z(2)) via the regulator (Chern class) map. The transcendental part of the regulator map is defined as an Abel
Failure of the Hasse principle on general K3 surfaces
 J. Inst. Math. Jussieu
, 2013
"... Abstract. We show that transcendental elements of the Brauer group of an algebraic surface can obstruct the Hasse principle. We construct a general K3 surface X of degree 2 over Q, together with a twotorsion Brauer class α that is unramified at every finite prime, but ramifies at real points of X. ..."
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Cited by 8 (2 self)
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Abstract. We show that transcendental elements of the Brauer group of an algebraic surface can obstruct the Hasse principle. We construct a general K3 surface X of degree 2 over Q, together with a twotorsion Brauer class α that is unramified at every finite prime, but ramifies at real points of X
On free profinite groups of uncountable rank
 In “Recent Developments in the Inverse Galois Problem
, 1995
"... Let C be an algebraically closed field, consider a transcendental element t over C, and let K = C(t). Douady [Dou] applies Riemann Existence theorem and a descent lemma of Grothendieck to prove that if char(C) = 0, then G(K) is the free profinite group F̂m, of rank m = card(C). In the case char(C) ..."
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Cited by 7 (3 self)
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Let C be an algebraically closed field, consider a transcendental element t over C, and let K = C(t). Douady [Dou] applies Riemann Existence theorem and a descent lemma of Grothendieck to prove that if char(C) = 0, then G(K) is the free profinite group F̂m, of rank m = card(C). In the case char
Results 1  10
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