An A-argument is the agent argument of a physical-effect verb ('kill', 'break').
This is often simply called "A" (or "A argument" without a hyphen). Note that here it refers to an argument type (a syntactic function, like "subject"), not to a semantic role (as in Croft 2022; and also in Bickel's work; see Haspelmath 2011).
A role (SEM) = the agent or agent-like central participant role in the prototypical bivalent event (that is, a breaking event) or the prototypical trivalent event (that is, a giving event). Examples: in Jack broke the window, Jack plays the A role in the breaking event; and in Jill gave Joe the keys, Jill plays the A role in the giving event. (Section 6.3.1)