NEW YORK — The last completed book we are likely to get from Maurice Sendak remembers a man he often insisted was the real genius of the family, his brother Jack.

Sendak died last May at age 83 after years of health problems, but he had managed to finish ‘‘My Brother’s Book,’’ published this week. Admirers of ‘‘Where the Wild Things Are’’ and other Sendak stories will recognize its themes of danger, flight, and fantasy, captured in a dreamy-scary swirl that demonstrates Sendak’s debt to William Blake.