Synonymous keyword retrieval has become an important problem for sponsored search ever since major search engines relax the exact match product's matching requirement to a synonymous level. Since the synonymous relations between queries and keywords are quite scarce, the traditional information retrieval framework is inefficient in this scenario. In this paper, we propose a novel quotient space-based retrieval framework to address this problem. Considering the synonymy among keywords as a mathematical equivalence relation, we can compress the synonymous keywords into one representative, and the corresponding quotient space would greatly reduce the size of the keyword repository. Then an embedding-based retrieval is directly conducted between queries and the keyword representatives. To mitigate the semantic gap of the quotient space-based retrieval, a single semantic siamese model is utilized to detect both the keyword--keyword and query-keyword synonymous relations. The experiments show that with our quotient space-based retrieval method, the synonymous keyword retrieving performance can be greatly improved in terms of memory cost and recall efficiency. This method has been successfully implemented in Baidu's online sponsored search system and has yielded a significant improvement in revenue.