Along with Stanisław Mazur, Mark Kac, Włodzimierz Stożek, Kuratowski, and others, Ulam was a member of the Lwów School of Mathematics.

In 1980, Donald Kerr, laboratory director at Los Alamos, with the strong support of Ulam and Mark Kac, founded the Center for Nonlinear Studies ( CNLS ).

The work he had on exhibit was entitled, Teleporting an Unknown State, a piece in which Kac enables a plant in a dark room to grow with light sent around the world through the Internet by remote participants.

In what is probably his most famous work, Alba, Kac commissioned a French laboratory to create a green-fluorescent rabbit ; a rabbit implanted with a Green Fluorescent Protein ( GFP ) gene from a type of jellyfish.

Kac's aim was for Alba to live with his family, but prior to the scheduled release of Alba to Kac, the lab retracted their agreement and decided that Alba should stay in the lab.

* The Role of Images and Aesthetic Experience in Bio Art: Eduardo Kac in conversation with Toni Hildebrandt

* Podcast interview with Eduardo Kac

In one of his works, Alba, Kac collaborated with a French laboratory to procure a green-fluorescent rabbit: a rabbit implanted with a green fluorescent protein gene from a type of jellyfish in order for the rabbit to fluoresce green under ultraviolet light.

Victor Kac was also studying simple or nearly simple Lie algebras with polynomial growth.

where the two Kac – Moody algebras in the right hand side are associated with the submatrices of C corresponding to the index sets I < sub > 1 </ sub > and I < sub > 2 </ sub >.

An important subclass of Kac – Moody algebras corresponds to symmetrizable generalized Cartan matrices C, which can be decomposed as DS, where D is a diagonal matrix with positive integer entries and S is a symmetric matrix.

The universal generalized Kac – Moody algebra with given symmetrized Cartan matrix is defined by generators and and and relations

Alba was the name of a genetically modified " glowing " rabbit created as an artistic work by contemporary artist Eduardo Kac, produced in collaboration with French geneticist Louis-Marie Houdebine.

If the manifold is a circle these are called loop groups, and have central extensions whose Lie algebras are ( more or less ) Kac – Moody algebras.

The last two are particularly interesting ( according to Kac ) because they have the standard model gauge group SU ( 3 ) xSU ( 2 ) xU ( 1 ) as their zero level algebra.

In 1997, Kac was one of the first human beings to have a RFID microchip implanted in his body.

These algebras form a generalization of finite-dimensional semisimple Lie algebras, and many properties related to the structure of a Lie algebra such as its root system, irreducible representations, and connection to flag manifolds have natural analogues in the Kac – Moody setting.

Kac – Moody algebras and generalized Kac – Moody algebras also have Cartan subalgebras.

Kac – Moody algebra, except that it is allowed to have imaginary simple roots.

Most generalized Kac – Moody algebras are thought not to have distinguishing features.

* Generalized Kac – Moody algebra, a Lie algebra that is similar to a Kac – Moody algebra, except that it is allowed to have imaginary simple roots

When Alba was exposed to such light, she would literally glow green — though photos by Kac showing the entire organism, including its hair, glowing a uniform green have had their veracity challenged.

defined Ree groups over infinite fields of characteristics 2 and 3. and introduced Ree groups of infinite-dimensional Kac – Moody algebras.

Eduardo Kac has described Alba as an animal that does not exist in nature.

The lowest weight representations that are not irreducible can be read off from the Kac determinant formula,

A generalized Kac – Moody algebra is obtained from a universal one by changing the Cartan matrix, by the operations of killing something in the center, or taking a central extension, or adding outer derivations.

and satisfies a few other easily checked technical conditions, then it is a generalized Kac – Moody algebra.

Properties of a Kac – Moody algebra are controlled by the algebraic properties of its generalized Cartan matrix C. In order to classify Kac – Moody algebras, it is enough to consider the case of an indecomposable matrixC, that is, assume that there is no decomposition of the set of indices I into a disjoint union of non-empty subsets I < sub > 1 </ sub > and I < sub > 2 </ sub > such that C < sub > ij </ sub > = 0 for all i in I < sub > 1 </ sub > and j in I < sub > 2 </ sub >.

* The Kac idea of Wick rotations.

However, Kac used GFP as a social marker, in a symbolic ( not scientific ) manner, to raise questions about how society constructs the idea of difference.

* Kac, Victor G. et al.

Alwyn Scott was its first director, and Kac was chairman of its first external advisory committee, on which Martin Kruskal also served.

Kac immediately said: " I cringe.

* Mark Kac and Stanislaw Ulam, Mathematics and Logic: Retrospect and Prospects, New York, Praeger, 1968.

It also forms the basis for the rigorous path integral formulation of quantum mechanics ( by the Feynman – Kac formula, a solution to the Schrödinger equation can be represented in terms of the Wiener process ) and the study of eternal inflation in physical cosmology.

* Kac, Victor, Vertex Algebras for Beginners, Second Edition, AMS 1997 ISBN 0-8218-0643-2.

However, according to M. Kac and E. Nelson, any kind of time development ( be it deterministic or essentially

Examples of infinite Coxeter groups include the triangle groups corresponding to regular tessellations of the Euclidean plane and the hyperbolic plane, and the Weyl groups of infinite-dimensional Kac – Moody algebras.

The simple complex finite dimensional Lie superalgebras were classified by Victor Kac.

* Kac, V. G. Lie superalgebras.

Harris's students in linguistics include, among many others, Joseph Applegate, Ernest Bender, Noam Chomsky, William Evan, Lila R. Gleitman, Michael Gottfried, Maurice Gross, James Higginbotham, Stephen B. Johnson, Aravind Joshi, Michael Kac, Edward Keenan, Daythal Kendall, Richard Kittredge, James A. Loriot / Lauriault, Leigh Lisker, Fred Lukoff, Paul Mattick, James Munz, Bruce E. Nevin, Jean-Pierre Paillet, Ellen Prince, John R. Ross, Naomi Sager, Morris Salkoff, Thomas A. Ryckman, and William C. Watt.