Use of the trace map for evaluating localization properties

1999 ◽  
Vol 59 (17) ◽  
pp. 11315-11321 ◽  
Author(s):  
Gerardo G. Naumis
Keyword(s):  
Trace Map

Totally Wild Quadratic Forms of Type E7

2017 ◽  
Author(s):  
Bernhard M¨uhlherr ◽  
Holger P. Petersson ◽  
Richard M. Weiss
Keyword(s):  
Division Algebra ◽  
Quadratic Forms ◽  
Quadratic Space ◽  
Trace Map ◽  
Quaternion Division Algebra

This chapter assumes that (K, L, q) is a totally wild quadratic space of type E₇. The goal is to prove the proposition that takes into account Λ‎ of type E₇, D as the quaternion division algebra over K whose image in Br(K) is the Clifford invariant of q, and the trace and trace map. The chapter also considers two other propositions: the first states that if the trace map is not equal to zero, then the Moufang residues R₀ and R₁ are not indifferent; the second states that if the trace map is equal to zero, then the Moufang residues R₀ and R₁ are both indifferent.

Trace-map invariant and zero-energy states of the tight-binding Rudin-Shapiro model

1992 ◽  
Vol 46 (6) ◽  
pp. 3296-3304 ◽  
Author(s):  
Mihnea Dulea ◽  
Magnus Johansson ◽  
Rolf Riklund
Keyword(s):  
Tight Binding ◽  
Zero Energy ◽  
Trace Map ◽  
Energy States

A Trace Map Attack Against Special Ring-LWE Samples

2021 ◽  
pp. 3-22
Author(s):  
Yasuhiko Ikematsu ◽  
Satoshi Nakamura ◽  
Masaya Yasuda
Keyword(s):  
Trace Map ◽  
Special Ring

scholarly journals Delocalized Eta Invariants, Algebraicity, and K-Theory of Group C*-Algebras

2019 ◽  
Author(s):  
Zhizhang Xie ◽  
Guoliang Yu
Keyword(s):  
Conjugacy Class ◽  
Discrete Group ◽  
Polynomial Growth ◽  
Algebraic Numbers ◽  
Eta Invariant ◽  
Trace Map ◽  
Novikov Conjecture ◽  
C Algebras ◽  
Eta Invariants ◽  
K Theory

Abstract In this paper, we establish a precise connection between higher rho invariants and delocalized eta invariants. Given an element in a discrete group, if its conjugacy class has polynomial growth, then there is a natural trace map on the $K_0$-group of its group $C^\ast$-algebra. For each such trace map, we construct a determinant map on secondary higher invariants. We show that, under the evaluation of this determinant map, the image of a higher rho invariant is precisely the corresponding delocalized eta invariant of Lott. As a consequence, we show that if the Baum–Connes conjecture holds for a group, then Lott’s delocalized eta invariants take values in algebraic numbers. We also generalize Lott’s delocalized eta invariant to the case where the corresponding conjugacy class does not have polynomial growth, provided that the strong Novikov conjecture holds for the group.

scholarly journals Algebraic K-theory of group rings and the cyclotomic trace map

2017 ◽  
Vol 304 ◽  
pp. 930-1020 ◽  
Author(s):  
Wolfgang Lück ◽  
Holger Reich ◽  
John Rognes ◽  
Marco Varisco
Keyword(s):  
Group Rings ◽  
Trace Map ◽  
K Theory

scholarly journals Trace map and regularity of finite extensions of a DVR

2017 ◽  
Vol 172 ◽  
pp. 133-144
Author(s):  
Fabio Tonini
Keyword(s):  
Trace Map

scholarly journals ON THE PRODUCT OF ELEMENTS WITH PRESCRIBED TRACE

2020 ◽  
pp. 1-25
Author(s):  
JOHN SHEEKEY ◽  
GEERTRUI VAN DE VOORDE ◽  
JOSÉ FELIPE VOLOCH
Keyword(s):  
Finite Fields ◽  
Complete Solution ◽  
Finite Extension ◽  
Finite Geometry ◽  
Nonlinear Functions ◽  
Irreducible Polynomials ◽  
Trace Map ◽  
Linear Sets

This paper deals with the following problem. Given a finite extension of fields $\mathbb{L}/\mathbb{K}$ and denoting the trace map from $\mathbb{L}$ to $\mathbb{K}$ by $\text{Tr}$ , for which elements $z$ in $\mathbb{L}$ , and $a$ , $b$ in $\mathbb{K}$ , is it possible to write $z$ as a product $xy$ , where $x,y\in \mathbb{L}$ with $\text{Tr}(x)=a,\text{Tr}(y)=b$ ? We solve most of these problems for finite fields, with a complete solution when the degree of the extension is at least 5. We also have results for arbitrary fields and extensions of degrees 2, 3 or 4. We then apply our results to the study of perfect nonlinear functions, semifields, irreducible polynomials with prescribed coefficients, and a problem from finite geometry concerning the existence of certain disjoint linear sets.

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