**Are you an EPFL student looking for a semester project?**

Work with us on data science and visualisation projects, and deploy your project as an app on top of GraphSearch.

Lecture# Correspondence between Heis and Co-adjoint Orbits

Description

This lecture explores the 1-1 correspondence between Heisenberg groups and the co-adjoint orbits, highlighting the relationship between Fleis and the co-adjoint of Heis in different contexts. The instructor discusses the significance of this correspondence in various mathematical frameworks, emphasizing the mapping between different mathematical structures.

Official source

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Related concepts (32)

Discrete mathematics

Discrete mathematics is the study of mathematical structures that can be considered "discrete" (in a way analogous to discrete variables, having a bijection with the set of natural numbers) rather than "continuous" (analogously to continuous functions). Objects studied in discrete mathematics include integers, graphs, and statements in logic. By contrast, discrete mathematics excludes topics in "continuous mathematics" such as real numbers, calculus or Euclidean geometry.

Philosophy of mathematics

The philosophy of mathematics is the branch of philosophy that studies the assumptions, foundations, and implications of mathematics. It aims to understand the nature and methods of mathematics, and find out the place of mathematics in people's lives. The logical and structural nature of mathematics makes this branch of philosophy broad and unique. The philosophy of mathematics has two major themes: mathematical realism and mathematical anti-realism. The origin of mathematics is of arguments and disagreements.

Bijection

In mathematics, a bijection, also known as a bijective function, one-to-one correspondence, or invertible function, is a function between the elements of two sets, where each element of one set is paired with exactly one element of the other set, and each element of the other set is paired with exactly one element of the first set; there are no unpaired elements between the two sets. In mathematical terms, a bijective function f: X → Y is a one-to-one (injective) and onto (surjective) mapping of a set X to a set Y.

Adjoint representation

In mathematics, the adjoint representation (or adjoint action) of a Lie group G is a way of representing the elements of the group as linear transformations of the group's Lie algebra, considered as a vector space. For example, if G is , the Lie group of real n-by-n invertible matrices, then the adjoint representation is the group homomorphism that sends an invertible n-by-n matrix to an endomorphism of the vector space of all linear transformations of defined by: . For any Lie group, this natural representation is obtained by linearizing (i.

E (mathematical constant)

The number e, also known as Euler's number, is a mathematical constant approximately equal to 2.71828 that can be characterized in many ways. It is the base of natural logarithms. It is the limit of (1 + 1/n)n as n approaches infinity, an expression that arises in the study of compound interest. It can also be calculated as the sum of the infinite series It is also the unique positive number a such that the graph of the function y = ax has a slope of 1 at x = 0.

Related lectures (32)

Constructing Correlators with Path Integrals

Explores constructing correlators using path integrals in quantum mechanics, focusing on the Euclidean and Minkowski spaces and the significance of imaginary time evolution.

Limits and Colimits in Functor CategoriesMATH-436: Homotopical algebra

Explores limits and colimits in functor categories, focusing on equalizers, pullbacks, and their significance in category theory.

Bernoulli convolutions: The dimension of Bernoulli convolutions

Explores the dimension of Bernoulli convolutions, discussing fair tosses and polynomial roots.

Quantum Field Theory: Fermions and Grassmann Numbers

Explores quantum field theory, focusing on fermions and Grassmann numbers in the path integral formalism.

Meromorphic Functions & DifferentialsMATH-410: Riemann surfaces

Explores meromorphic functions, poles, residues, orders, divisors, and the Riemann-Roch theorem.