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Infinite dimensional non-affine Kac-Moody algebras are said to be of Indefinite type. Their structure and representation theory resembles that of the familiar finite dimensional simple Lie algebras, except that finite entities now become infinite (e.g infinite sums, infinite dimension etc). I will talk about some of these differences and show that in spite of these infinities, one can still define a notion of a "representation ring" R(X) for an Indefinite type Kac-Moody algebra X.

Then, in analogy with the series A_n, B_n, C_n, D_n of finite dimensional simple Lie algebras, we consider series X_n of Indefinite Kac-Moody algebras. We will see how the operation of stable tensor product for X_n (i.e as n--> infinity) can be obtained from the rings R(X_n) using filtrations and direct limits.