Formal groups and buds

1975 ◽  
pp. 31-57
Author(s):  
Michel Lazard
Keyword(s):  
Formal Groups

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.

scholarly journals p-adic Measures and Formal Groups

1993 ◽  
Vol 44 (3) ◽  
pp. 340-351 ◽  
Author(s):  
N. Childress
Keyword(s):  
Formal Groups

scholarly journals On formal groups and Tate cohomology in local fields

2018 ◽  
Vol 182 (3) ◽  
pp. 285-299
Author(s):  
Nils Ellerbrock ◽  
Andreas Nickel
Keyword(s):  
Local Fields ◽  
Formal Groups ◽  
Tate Cohomology

scholarly journals A note on extensions of algebraic and formal groups, III

1997 ◽  
Vol 49 (2) ◽  
pp. 241-257 ◽  
Author(s):  
Tsutomu Sekiguchi ◽  
Noriyuki Suwa
Keyword(s):  
Formal Groups

scholarly journals Explicit form of the Hilbert symbol for polynomial formal groups

2015 ◽  
Vol 26 (5) ◽  
pp. 785-796 ◽  
Author(s):  
S. Vostokov ◽  
V. Volkov
Keyword(s):  
Explicit Form ◽  
Hilbert Symbol ◽  
Formal Groups
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