分支环，疏环，树包络环
Branch Rings, Thinned Rings, Tree Enveloping Rings
摘要：
我们发展理论的"分支代数“，这是无限维的结合代数是同构的，直到采取子环的有限余维，一个矩阵环本身。主要的例子来自群体对树木的作用。特别地，对于每个域k，我们构造一个k-代数K，它（1）是无限维的，但只有有限维的子代数;（2）有一个有限余维的子代数，同构于$M_2(K)$ ;（3）是素的;（4）有二次增长，因此Gelfand-Kirillov维数为2;（5）是递归的;（6）不满足恒等式;（7）包含一个超越可逆元;（8）是半本原的，如果k具有特征$\neq2$ ;（9）是分次的，如果k具有特征2;（10）是本原的，如果k是GF（2）的一个非代数扩张;（11）是分次nil和Jacobson根，如果k是GF（2）的一个代数扩张。
英文摘要：
We develop the theory of ``branch algebras'', which are infinite-dimensional associative algebras that are isomorphic, up to taking subrings of finite codimension, to a matrix ring over themselves. The main examples come from groups acting on trees. In particular, for every field k we construct a k-algebra K which (1) is finitely generated and infinite-dimensional, but has only finite-dimensional quotients; (2) has a subalgebra of finite codimension, isomorphic to $M_2(K)$; (3) is prime; (4) has quadratic growth, and therefore Gelfand-Kirillov dimension 2; (5) is recursively presented; (6) satisfies no identity; (7) contains a transcendental, invertible element; (8) is semiprimitive if k has characteristic $\neq2$; (9) is graded if k has characteristic 2; (10) is primitive if k is a non-algebraic extension of GF(2); (11) is graded nil and Jacobson radical if k is an algebraic extension of GF(2).
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