Decision-making is a fundamental capability in everyday life. Large Language Models (LLMs) provide multifaceted support in enhancing human decision-making processes. However, understanding the influencing factors of LLM-assisted decision-making is crucial for enabling individuals to utilize LLM-provided advantages and minimize associated risks in order to make more informed and better decisions. This study presents the results of a comprehensive literature analysis, providing a structural overview and detailed analysis of determinants impacting decision-making with LLM support. In particular, we explore the effects of technological aspects of LLMs, including transparency and prompt engineering, psychological factors such as emotions and decision-making styles, as well as decision-specific determinants such as task difficulty and accountability. In addition, the impact of the determinants on the decision-making process is illustrated via multiple application scenarios. Drawing from our analysis, we develop a dependency framework that systematizes possible interactions in terms of reciprocal interdependencies between these determinants. Our research reveals that, due to the multifaceted interactions with various determinants, factors such as trust in or reliance on LLMs, the user's mental model, and the characteristics of information processing are identified as significant aspects influencing LLM-assisted decision-making processes. Our findings can be seen as crucial for improving decision quality in human-AI collaboration, empowering both users and organizations, and designing more effective LLM interfaces. Additionally, our work provides a foundation for future empirical investigations on the determinants of decision-making assisted by LLMs.