In mathematics, a Casimir element (also known as a Casimir invariant or Casimir operator) is a distinguished element of the center of the universal enveloping algebra of a Lie algebra. A prototypical example is the squared angular momentum operator, which is a Casimir element of the three-dimensional rotation group.
More generally, Casimir elements can be used to refer to any element of the center of the universal enveloping algebra. The algebra of these elements is known to be isomorphic to a polynomial algebra through the Harish-Chandra isomorphism.
The Casimir element is named after Hendrik Casimir, who identified them in his description of rigid body dynamics in 1931.[1]
^Oliver, David (2004). The shaggy steed of physics: mathematical beauty in the physical world. Springer. p. 81. ISBN 978-0-387-40307-6.
In mathematics, a Casimirelement (also known as a Casimir invariant or Casimir operator) is a distinguished element of the center of the universal enveloping...
provide important information about the representations. The quadratic Casimirelement is of particular importance in this regard. Although the canonical...
is compact and simple of rank 1, and so it has a single independent Casimirelement, a quadratic invariant function of the three generators which commutes...
Representation of a Lie superalgebra Universal enveloping algebra Casimirelement Infinitesimal character Harish-Chandra homomorphism Fundamental representation...
Casimir I the Restorer (Polish: Kazimierz I Odnowiciel; 25 July 1016 – 19 March 1058), a member of the Piast dynasty, was the duke of Poland from 1040...
can be far fewer terms to sum. The formula is based on use of the Casimirelement and its derivation is independent of the character formula. It states...
representation). Finally, there is also a formula for the eigenvalue of the Casimirelement, which acts as a scalar in each irreducible representation. Although...
representation theory of semisimple Lie algebras. Casimirelement A Casimirelement is a distinguished element of the center of the universal enveloping algebra...
that Courtois is the first one to isolate the element. In 1873, the French medical researcher Casimir Davaine (1812–1882) discovered the antiseptic action...
of Twentieth-Century Art". Encyclopedia.com. Retrieved 18 March 2014. "Casimir Malevich, The Columbia Encyclopedia, Sixth Edition". Encyclopedia.com....
contributions, in particular to quantum electrodynamics, where he calculated the Casimir force in an arbitrary macroscopic configuration of metals and dielectrics...
attacked Poland and prevented Casimir IV Jagiellon, King of Poland, from supporting Peter Aaron, but eventually acknowledged Casimir's suzerainty in 1459. Stephen...
this is an abuse of terminology since an ordered pair need not be an element of a vector space.) The entries of an ordered pair can be other ordered...
Kingdom of Galicia–Volhynia from 1272 to 1349, when it was conquered by King Casimir III the Great of Poland. From 1434, it was the regional capital of the...
(named after Euclidean manifold, a structure of Riemannian manifold). The Casimir effect shows that quantum field theory allows the energy density in certain...
invariant form, as are all other forms obtained from Casimir operators. The derivation of Casimir operators vanishes; for the Killing form, this vanishing...
constant for this element, Z {\displaystyle Z} is the atomic number, i.e. the number of protons in the atomic nucleus of this element, n 1 {\displaystyle...
and are built of words meaning "fighter", "war", or "anger". Examples: Casimir, Vladimir, Sambor, Wojciech and Zbigniew. Many of them derive from the...
proposing the concept of electron spin, Jan Tinbergen, Arend Rutgers, Hendrik Casimir, Gerhard Dieke, Dirk Struik, and Gerard Kuiper. His assistants included...
approach to quantum electrodynamics 1948 Hendrik Casimir predicts a rudimentary attractive Casimir force on a parallel plate capacitor 1951 Martin Deutsch...
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