For a locally compact group G and a compact subgroup K, the corresponding Hecke algebra consists of all continuous compactly supported complex functions on G that are K–bi-invariant. There are many examples of totally disconnected locally compact groups whose Hecke algebras with respect to a maximal compact subgroups are not commutative. One of those is the universal group U(F)⁺, when F is primitive but not 2–transitive. For this class of groups we prove the Hecke algebra with respect to a maximal compact subgroup K is infinitely generated and infinitely presented. This may be relevant for constructing irreducible unitary representations of U(F)⁺ whose subspace of K–fixed vectors has dimension at least two. On the contrary, when F is 2–transitive that Hecke algebra of U(F)⁺ is commutative, finitely generated admitting a single generator.

对于局部紧致群G和紧致子群K，相应的Hecke代数包括G上所有连续的，紧致支持的复函数，它们都是K-双不变的。有许多完全断开的局部紧致群的例子，它们的最大代数子群的Hecke代数不是可交换的。其中之一是通用群U（F）⁺，其中F是原始的，而不是2-可及的。对于这类组，我们证明关于最大紧致子组K的Hecke代数是无限生成和无限呈现的。这可能与构造U（F）⁺的不可约unit表示有关，后者的K个固定向量的子空间的维数至少为2。相反，当F是2传递的时，U（F）^+的Hecke代数是可交换的，因此它是有限生成的，允许一个生成器。