Finite Groups Representation Theory with Coq

نویسنده

  • Sidi Ould Biha
چکیده

Representation theory is a branch of algebra that allows the study of groups through linear applications, i.e. matrices. Thus problems in abstract groups can be reduced to problems on matrices. Representation theory is the basis of character theory. In this paper we present a formalization of finite groups representation theory in the Coq system that includes a formalization of Maschke’s theorem on reducible finite group algebra.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

The Rooster and the Butterflies

This paper describes a machine-checked proof of the JordanHölder theorem for finite groups. This purpose of this description is to discuss the representation of the elementary concepts of finite group theory inside type theory. The design choices underlying these representations were crucial to the successful formalization of a complete proof of the Odd Order Theorem with the Coq system.

متن کامل

Finitary-based Domain Theory in Coq: An Early Report

In his "Lectures on a Mathematical Theory of Computation" [5], Dana Scott formulated domains in terms of neighborhood systems. Later, Scott favored a formulation in terms of information systems [6] but has not rewritten his lectures notes. Cartwright and Parsons later revised Scott’s lecture notes to reflect a formulation of domains in terms of ‘finitary basis’ [3], where a finitary basis is an...

متن کامل

A Modular Formalisation of Finite Group Theory

In this paper, we present a formalisation of elementary group theory done in Coq. This work is the first milestone of a long-term effort to formalise Feit-Thompson theorem. As our further developments will heavily rely on this initial base, we took special care to articulate it in the most compositional way. Key-words: finite groups, proof assistants, formalisation of mathematics ∗ Microsoft Re...

متن کامل

Simulating Finite Eilenberg Machines with a Reactive Engine

Eilenberg machines have been introduced in 1974 in the field of formal language theory. They are finite automata for which the alphabet is interpreted by mathematical relations over an abstract set. They generalize many finite state machines. We consider in the present work the subclass of finite Eilenberg machines for which we provide an executable complete simulator. This program is specified...

متن کامل

A Constructive Theory of Regular Languages in Coq

We present a formal constructive theory of regular languages consisting of about 1400 lines of Coq/Ssreflect. As representations we consider regular expressions, deterministic and nondeterministic automata, and Myhill and Nerode partitions. We construct computable functions translating between these representations and show that equivalence of representations is decidable. We also establish the...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2009