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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In abstract algebra, a representation of a Hopf algebra is a representation of its underlying associative algebra. That is, a representation of a Hopf algebra H over a field K is a K-vector space V with an action H × V V usually denoted by juxtaposition (that is, the image of (h,v) is written hv). The vector space V is called an H-module.