Communications in Information and Systems

Volume 15 (2015)

Number 4

Some solvable stochastic differential games in $SU(3)$

Pages: 477 – 487



Tyrone E. Duncan (Department of Mathematics, University of Kansas, Lawrence, Ks., U.S.A.)

Bozenna Pasik-Duncan (Department of Mathematics, University of Kansas, Lawrence, Ks., U.S.A.)


Some stochastic differential games are formulated and explicitly solved in the special unitary group $SU(3)$. This Lie group is probably the most elementary simple Lie group of rank two, that is, the Cartan subalgebra has dimension two. The game is to influence the roots of $SU(3)$ which are directly related to the eigenvalues of an element in $SU(3)$. The group $SU(3)$ has particular interest in physics because the Gell–Mann matrices are generators for $SU(3)$ that mediate Quantum Chromodynamics (QCD) which is also known as the Strong Force. Since the radial parts of Laplacians for higher rank Lie groups have a similar structure as the radial part of the Laplacian for $SU(3)$, stochastic differential games for $SU(3)$ are important to understand for extensions of possible solvable stochastic differential games for other Lie groups.

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