On formal groups in characteristic p

1975 ◽  
pp. 163-199
Author(s):  
Michel Lazard
Keyword(s):  
Characteristic P ◽  
Formal Groups

scholarly journals Counterexamples to Hochschild-Kostant-Rosenberg in characteristic p

2021 ◽  
Vol 9 ◽  
Author(s):  
Benjamin Antieau ◽  
Bhargav Bhatt ◽  
Akhil Mathew
Keyword(s):  
Spectral Sequence ◽  
Spectral Sequences ◽  
Characteristic P ◽  
De Rham

Abstract We give counterexamples to the degeneration of the Hochschild-Kostant-Rosenberg spectral sequence in characteristic p, both in the untwisted and twisted settings. We also prove that the de Rham-HP and crystalline-TP spectral sequences need not degenerate.

Effect of oxygen vacancies and crystal symmetry on piezocatalytic properties of Bi2WO6 ferroelectric nanosheets for wastewater decontamination

2021 ◽  
Author(s):  
Zihan Kang ◽  
Enzhu Lin ◽  
Ni Qin ◽  
Jiang Wu ◽  
Baowei Yuan ◽  
...  
Keyword(s):  
Organic Pollutants ◽  
Oxygen Vacancies ◽  
Mechanical Energy ◽  
Crystal Symmetry ◽  
Characteristic P ◽  
Novel Technique ◽  
Effect Of Oxygen

Piezocatalysis emerged as a novel technique to make use of mechanical energy in dealing with organic pollutants in wastewater. In this work, the ferroelectric Bi2WO6 (BWO) nanosheets with a characteristic...

scholarly journals SUBALGEBRAS OF THE POLYNOMIAL ALGEBRA IN POSITIVE CHARACTERISTIC AND THE JACOBIAN

2011 ◽  
Vol 10 (04) ◽  
pp. 605-613
Author(s):  
ALEXEY V. GAVRILOV
Keyword(s):  
Principal Ideal ◽  
Positive Characteristic ◽  
Polynomial Algebra ◽  
Characteristic P ◽  
The Ideal

Let 𝕜 be a field of characteristic p > 0 and R be a subalgebra of 𝕜[X] = 𝕜[x1, …, xn]. Let J(R) be the ideal in 𝕜[X] defined by [Formula: see text]. It is shown that if it is a principal ideal then [Formula: see text], where q = pn(p - 1)/2.

THE RAMIFICATION GROUPS AND DIFFERENT OF A COMPOSITUM OF ARTIN–SCHREIER EXTENSIONS

2010 ◽  
Vol 06 (07) ◽  
pp. 1541-1564 ◽  
Author(s):  
QINGQUAN WU ◽  
RENATE SCHEIDLER
Keyword(s):  
Class Number ◽  
Function Field ◽  
Positive Characteristic ◽  
Field Extension ◽  
Constant Field ◽  
Divisor Class ◽  
Characteristic P ◽  
Similar Nature ◽  
Field Of Positive Characteristic ◽  
The Ideal

Let K be a function field over a perfect constant field of positive characteristic p, and L the compositum of n (degree p) Artin–Schreier extensions of K. Then much of the behavior of the degree pn extension L/K is determined by the behavior of the degree p intermediate extensions M/K. For example, we prove that a place of K totally ramifies/is inert/splits completely in L if and only if it totally ramifies/is inert/splits completely in every M. Examples are provided to show that all possible decompositions are in fact possible; in particular, a place can be inert in a non-cyclic Galois function field extension, which is impossible in the case of a number field. Moreover, we give an explicit closed form description of all the different exponents in L/K in terms of those in all the M/K. Results of a similar nature are given for the genus, the regulator, the ideal class number and the divisor class number. In addition, for the case n = 2, we provide an explicit description of the ramification group filtration of L/K.

scholarly journals Formal groups and Z -entropies

2016 ◽  
Vol 472 (2195) ◽  
pp. 20160143 ◽  
Author(s):  
Piergiulio Tempesta
Keyword(s):  
Algebraic Topology ◽  
Formal Group ◽  
Point Of View ◽  
Trace Form ◽  
Formal Groups ◽  
Form Class ◽  
New Family ◽  
Mathematical Properties ◽  
Composition Process ◽  
Group Law

We shall prove that the celebrated Rényi entropy is the first example of a new family of infinitely many multi-parametric entropies. We shall call them the Z-entropies . Each of them, under suitable hypotheses, generalizes the celebrated entropies of Boltzmann and Rényi. A crucial aspect is that every Z -entropy is composable (Tempesta 2016 Ann. Phys. 365 , 180–197. ( doi:10.1016/j.aop.2015.08.013 )). This property means that the entropy of a system which is composed of two or more independent systems depends, in all the associated probability space, on the choice of the two systems only. Further properties are also required to describe the composition process in terms of a group law. The composability axiom, introduced as a generalization of the fourth Shannon–Khinchin axiom (postulating additivity), is a highly non-trivial requirement. Indeed, in the trace-form class, the Boltzmann entropy and Tsallis entropy are the only known composable cases. However, in the non-trace form class, the Z -entropies arise as new entropic functions possessing the mathematical properties necessary for information-theoretical applications, in both classical and quantum contexts. From a mathematical point of view, composability is intimately related to formal group theory of algebraic topology. The underlying group-theoretical structure determines crucially the statistical properties of the corresponding entropies.

COMMUTATOR IDENTITIES ON SYMMETRIC ELEMENTS OF GROUP ALGEBRAS

2013 ◽  
Vol 12 (08) ◽  
pp. 1350044
Author(s):  
TIBOR JUHÁSZ ◽  
ENIKŐ TÓTH
Keyword(s):  
Direct Product ◽  
Group Algebra ◽  
Group Algebras ◽  
Augmentation Ideal ◽  
Characteristic P ◽  
Derived Length ◽  
Commutator Identity ◽  
Nilpotency Index ◽  
Powerful Group

Let K be a field of odd characteristic p, and let G be the direct product of a finite p-group P ≠ 1 and a Hamiltonian 2-group. We show that the set of symmetric elements (KG)* of the group algebra KG with respect to the involution of KG which inverts all elements of G, satisfies all Lie commutator identities of degree t(P) or more, where t(P) denotes the nilpotency index of the augmentation ideal of the group algebra KP. In addition, if P is powerful, then (KG)* satisfies no Lie commutator identity of degree less than t(P). Applying this result we get that (KG)* is Lie nilpotent and Lie solvable, and its Lie nilpotency index and Lie derived length are not greater than t(P) and ⌈ log 2 t(P)⌉, respectively, and these bounds are attained whenever P is a powerful group. The corresponding result on the set of symmetric units of KG is also obtained.

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