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Artificial intelligence is becoming increasingly embedded in business management, influencing decisions in strategy, operations, marketing, human resources, finance, and organizational control. Its managerial significance no longer lies only in its capacity to process information faster than humans, but in its growing ability to recommend, rank, predict, allocate, and sometimes decide. This shift raises important questions about how organizations should govern AI when it begins to affect managerial judgment itself. The central problem addressed in this review is that management research has often treated AI as a performance-enhancing tool while giving less sustained attention to its governance consequences. Three tensions remain particularly fragmented: the delegation of decision authority to algorithmic systems, the maintenance of organizational accountability in distributed human-machine arrangements, and the conditions under which managers trust or distrust AI-assisted decisions. These issues are analytically distinct but practically interdependent. The objective of this critical review is to synthesize literature on AI in business management through the integrated lenses of authority, accountability, and trust. Rather than presenting AI adoption as an inevitable route to efficiency, the review interrogates the organizational assumptions behind AI-enabled decision-making. It asks how AI changes managerial discretion, responsibility, oversight, and confidence in organizational decisions. The review concludes that AI governance in management must move beyond technical performance and address the institutional conditions under which AI-assisted decisions are authorized, explained, contested, and trusted. Authority, accountability, and trust should not be treated as separate implementation concerns but as a connected governance triad. Future management research should therefore conceptualize AI not merely as a tool, but as a socio-technical actor that reshapes managerial responsibility and organizational control.